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Why would Kathril, Aspect Warper's ability grant multiple hexproof counters?
Kathril, Aspect Warper has this ability:

When Kathril, Aspect Warper enters the battlefield, put a flying counter on any creature you control if a creature card in your graveyard has flying. Repeat this process for first strike, double strike, deathtouch, hexproof, indestructible, lifelink, menace, reach, trample, and vigilance. Then put a +1/+1 counter on Kathril for each counter put on a creature this way.

There is a ruling in Gatherer that is confusing to me:

If cards in your graveyard have multiple hexproof abilities (such as hexproof, hexproof from white, and hexproof from black), a counter of each variant kind will be put onto a creature.

Why would this be true under the ability's wording and the rules?

702.11d “Hexproof from [quality]” is a variant of the hexproof ability. “Hexproof from [quality]” on a permanent means “This permanent can’t be the target of [quality] spells your opponents control or abilities your opponents control from [quality] sources.” A “hexproof from [quality]” ability is a hexproof ability.

So we see that "Hexproof from white" is a hexproof ability, thus is would count for Kathril's ability. I would assume that "Repeat this process for..." means that you do this action:

put a flying counter on any creature you control if a creature card in your graveyard has flying

but replace "flying" with the keyword that you are repeating the action for. As we go down the list, we eventually repeat the action for hexproof, so we follow this instruction:

put a hexproof counter on any creature you control if a creature card in your graveyard has hexproof

Due to 702.11d, if you have a creature with hexproof from white in your graveyard, that would count as having hexproof just the same as if you had a creature with normal hexproof in your graveyard. In either case, the instruction you are following then is to "put a hexproof counter on any creature you control".
How can these set of instructions cause you to put a "hexproof from white" counter on a creature you control? There doesn't appear to be any instruction to ever put a "hexproof from white" counter on a creature you control.
Does somehow "repeat this process for hexproof" actually mean "repeat this process for hexproof and every possible hexproof variant"?
Same question for Odric, Lunarch Marshal:

At the beginning of each combat, creatures you control gain first strike until end of turn if a creature you control has first strike. The same is true for flying, deathtouch, double strike, haste, hexproof, indestructible, lifelink, menace, reach, skulk, trample, and vigilance.

Again I would think that by a literal reading of the wording, if a creature you control has "hexproof from white" then this would cause all of your creatures yo be granted normal hexproof (they gain hexproof if a creature you control has hexproof; and having hexproof from white counts). But the rulings say the same as Kathril.

Kathril will create a separate counter for each variant of hexproof creatures in your graveyard have. In the same vein, Odric will give your creatures each variant of hexproof a creature you control have.
The reason Kathril, Odric and cards similar to them work the way they do is because of the following rule:

702.1c. An effect may state that "the same is true for" a list of keyword abilities or similar. If one of those keyword abilities has variants or variables and the effect grants that keyword or counters of that keyword to one or more objects and/or players, it grants each appropriate variant and variable of that keyword.

Add to that the rule saying

702.11d. "Hexproof from [quality]" is a variant of the hexproof ability [...]

and we see why Kathril gives "hexproof from" counters and Odric gives "hexproof from" to creatures. If we look at the definition of landwalk,

702.14a. Landwalk is a generic term that appears within an object's rules text as "[type]walk," where [type] is usually a subtype, but can be the card type land, any land type, any supertype, or any combination thereof.

I think you'll agree that plainswalk, islandwalk etc. are variants of landwalk, and thus Cairn Wanderer gains all that are present (with the same reasoning used for protection).

While the citations are nice, this answer might be nicer if you decoupled it from the other answer and gave a ruling summary first.

@JonTheMon Thanks for the tip! I didn't feel a summary was really necessary, since the asker already knows the result and was just asking for the explanation. It makes the answer more self-sufficient though, so I added it anyway. And yeah, on reflection adressing another answer just stands in the way. Edited!

When I first read this answer I was thrown off by 702.1c talking about the wording "the same is true for" while Kathril uses the wording "Repeat this process for". But I realized that 701.2c is in the keyword abilities section, so the "or similar" at the end of the first sentence is referring to the phrase "the same is true for", and not to "a list of keyword abilities". Therefore, that rule also applies to similar effects that iterate over a list of keyword abilities, including Kathril's.

When Kathril says "Repeat this process for hexproof", it actually reads "Repeat this process for hexproof and all its variants". As printed, "hexproof" refers to the category of hexproof abilities, not to the individual hexproof ability which would be different from e.g. "Hexproof from white".
Abilities are grouped under what I would call categories. For example, Mountainwalk, Islandwalk etc. are grouped under "Landwalk". You will not find a creature in Gatherer with the "Landwalk" ability, it's always "[basic land type]walk", or "[quality] landwalk". However, cards can still reference the Landwalk category, such as Hammerheim, and you mentally unroll that "landwalk" category into all the possible, individual landwalk abilities.
Another example: Protection. Cairn Wanderer has an ability very similar to Kathril's, and it references Protection. Protection is the name of the category protection, but no creature will ever have the plain "Protection" ability, because the correct form for protection abilities reads "Protection from [quality]".
There are unproblematic ability categories whose abilities have no variants, so there is no need to differentiate. Examples include flying, trample, first strike, and so on.
Hexproof seems to be the only ability with multiple variants but whose category name is also a legal name for one of its variants. This is the unfortunate  source of the confusion.
Kathril and similar cards like Cairn Wanderer reference categories, and you have to unroll their individual abilities. For Cairn Wanderer, it's obvious how it should work, Cairn Wanderer will never have "landwalk" or "protection", but only "mountainwalk" or "protection from black" as applicable. The same goes for Kathril and hexproof, with the unfortunately necessary caveat that you have to consciously separate the category "Hexproof" from its actual abilities.

Why would protection cause any counter to be placed? Protection isn't listed in the abilities list for Kathril (or Odric; though I see that it does apply to Cairn).

The protection argument from the Cairn example also applies to landwalk.

I thought about it some more and will rewrite the answer.

I don't know if there's a card with an example, but to be clear, if an ability simply said "put a hexproof counter on any creature you control if a creature card in your graveyard has hexproof" (no "repeat this for" bit), then it would still do the same thing; possibly add multiple hexproof counters, one for each variant of hexproof in your graveyard?

Pretty sure it would work like that, yes, but it would depend on the wording. As I said, Hexproof is an unfortunate outlier because it's both a category and an individual ability in that category, and you can't blindly tell which of them a card references.

You could always picture such a hypothetical card and replace "hexproof" with e.g. "landwalk", and once more with "forestwalk" and decide which one sounds more correct. If "Landwalk" sounds correct, then you would place all applicable counters, otherwise only that specific counter.

I guess the part that's most confusing here is that there is only an instruction to place a single counter in this hypothetical case (or the non-hypothetical case of Kathril when you don't have anything other than Hexproof). So a single "place a hexproof counter" instruction actually ends up causing you to place multiple counters... that just seems wrong.

@Gendolkari ignoring for a moment the fact that ruling on fictional cards isn't all that possible, no, that ability you made up would give a plain hexproof counter, regardless of which hexproof variant you control. Maybe my answer clears things up a bit? I feel Hackworth's explanation breaks down the more we dig into it.


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Why were the rules for Proliferate changed?
With the release of War of the Spark, the rules for Proliferate changed. Previously, they allowed you to add 1 counter to the chosen permanents and players, of a type it already had. Now, it adds an additional counter for every type of counter already present.
This seems like a big change that suddenly changes the way a bunch of existing cards work; in most cases making all of those cards stronger. Why alter the power level of all those existing cards?
It almost seems like if they one day said that from now on, "Lifelink" means that you get 2 life for every damage instead of 1.
In this article about War of the Spark rules changes, it mentions that the rules were changed:

The rules for proliferate got a makeover! The rule reminding you who chooses counters is dropped, since there are no more choices on the counters, and the other two rules are updated to match the new reality.

But this seems to be a change just to deal with the fact that "Proliferate" changed; it's not an explanation of the fact that Proliferate changed or why.
Is there an article or source that announces and explains this change?

I think you're certainly correct in theory, especially considering past changes in the game that were causing issues with minor changes by comparison. However in practice, I don't think the situation of wanting to add more than one counter is going to come up all that often - and when there is a deck that benefits from it, Proliferate was very likely already a game changer for it before. For some situations, it can even be a nerf, such as your Infect Commander deck now having to make a choice playing against an experience counter commander.

According to a post from Mark Rosewater (Lead Designer for Magic: The Gathering), the reasons were to make the mechanic as a whole more easily understandable, along with seemingly wanting to streamline the experience in digital MtG games.
Quoting the post in its entirety both for reference and relevance:

R&D is always on the lookout for ways to make cleaner, more straight-forward mechanics. This makes mechanics easier to process in tabletop and lessens the amounts of clicks on digital.
When we decided to bring back proliferate, we realized we could make a simple change that would both, on average, make the mechanic more powerful and clean it up for digital.
Previously if a player or creature had more than one counter, you the owner of the proliferating source chose which one of the different counters to duplicate. This new version doesn’t make you chose, but instead duplicates all of them. Remember, you still choose which players and/or permanents to proliferate.
Yes, there’s a tiny scenario where you have to chose between duplicating both a positive and a negative counter, but that’s far less likely than the scenario where you have two different types of counters you want to duplicate (especially on creatures as +1/+1 counters and -1/-1 counters negate one another).

On the issue of + and - counters on the same creature: I was under the impression, that those countered each other out and would be taken of the creature?

@Erik You are right in your assessment. It can easily occur for players, though, if they have energy or experience counters and poison counters, for instance.

Or a Gideon with a +1/+1 and loyality counters, I see. Thank you.

@Erik Yes the point was that it's not very likely for a creature to have both a good and a bad counter at the same time, because the most common type of good and bad counters that show up on creatures can't both exist at the same time.

@Erik If we take "positive" to mean "good" and "negative" to mean "bad", then not all positive counters cancel out with negative counters.

@Acccumulation I read Erik's comment as being specifically about +1/+1 and -1/-1 counters, abbreviated as + and -, not generically "good" and "bad"

@Caleth Yes, as did I. And I was pointing out that the "positive" and "negative" mentioned in the answer were not restricted to +1/+1 and -1/-1.

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Which spells or abilities are affected by things that care about targeting?
Note: this is intended to be a canonical question about whether or not a spell or ability targets so there are multiple sub-questions.

Can Hexproof or Shroud save my creature from Wrath of God? What about a Cyclonic Rift that was cast for it's Overload cost?

Does shroud prevent me from using the Monstrosity ability of a creature, or from giving it more counters with Proliferate?

Can I cast an Aura Enchantment on one of my creatures with Shroud, or an opponent's creature with Hexproof? Or can I use the Equip ability to attach an equipment to one of my creatures with Shroud?

Will Diffusion Sliver's ability trigger when my opponent plays Wrath of God? And will I have to sacrifice my Phantasmal Image if my opponent casts Nausea?

Will Shroud or Hexproof prevent an opponent from choosing me with Stuffy Doll's ability?

Will Hexproof keep one of my creatures from being affected by Sleep?

If an Aura or Equipment is attached to a creature with Hexproof, does the Hexproof protect the attached permanent?

Can Redirect change Burn Down the House to only target a single creature instead?

One example different from the others: spells with replicate are blocked by shroud/hexproof

@Zags I don't understand, why would replicate make any difference at all?

Replicate/strive don't change how a spell interacts with hexproof/shroud, but that's why they're notable, especially in contrast to overload (Electrickery and Pyromatics have very similar looking text but very different behavior, especially with regard to hexproof/shroud).  Spells with replicate or strive fall into the mental category of "I can use this to hit all of my opponents stuff" but are different from other things in this category in that they still target each permanent.

I guess I wouldn't have thought of replicate as causing possible confusion, because it creates copies of the spell; so you simply end up with multiple spells that each say "Pyromatics deals 1 damage to any target." The fact that those spells were created with replicate, instead of by simply casting Pyromatics repeatedly, seems inconsequential.

The answer to all of these questions is no.
Hexproof and Shroud only prevent "targeting"; there are many ways for a spell or ability to affect something without that something being a "target".

702.11b “Hexproof” on a permanent means “This permanent can’t be the target of spells or abilities your opponents control.”
702.18a Shroud is a static ability. “Shroud” means “This permanent or player can’t be the target of spells or abilities.”

The important thing here is to keep in mind that when Magic uses the word "target", it is using a specific rules-defined term; it is not just the English word that can mean "a thing you go after or attack".

114.10a Just because an object or player is being affected by a spell or ability doesn’t make that object or player a target of that spell or ability. Unless that object or player is identified by the word “target” in the text of that spell or ability, or the rule for that keyword ability, it’s not a target.

A spell or ability only targets the things it is affecting in the following 3 situations:

It uses the word "target" in the text of the spell or ability.

114.1a An instant or sorcery spell is targeted if its spell ability identifies something it will affect by using the phrase “target [something],” where the “something” is a phrase that describes an object and/or player.
114.1c An activated ability is targeted if it identifies something it will affect by using the phrase “target [something],” where the “something” is a phrase that describes an object and/or player.
114.1d A triggered ability is targeted if it identifies something it will affect by using the phrase “target [something],” where the “something” is a phrase that describes an object and/or player.

It uses a keyword that has the word "target" in the rules text, such as "Equip".

114.1e Some keyword abilities, such as equip and provoke, represent targeted activated or triggered abilities. In those cases, the phrase “target [something]” appears in the rule for that keyword ability rather than in the ability itself. (The keyword’s reminder text will often contain the word “target.”)

It is an Aura spell, which by the rules are always targeted spells (targeting the object that you want to enchant).

114.1b Aura spells are always targeted.

(Note that Aura spells are only targeted when they are cast; if an Aura is entering the battlefield through some other means, it could be attached to a creature without targeting that creature).
If a spell or ability is none of the above, it does not target, and thus is not affected by Hexproof or Shroud. Even if the spell or ability tells you to “choose” something.
For the specific questions/examples given:

Wrath of God can destroy creatures with Hexproof or Shroud because it does not contain the word "target".
Cyclonic Rift is normally targeted, but if it was cast for the Overload cost, then the word "target" is replaced with the word "each", so the spell as it exists on the stack doesn't contain the word "target".
Monstrosity does not target the permanent it affects, because "target" does not appear in the rules text for it.
Proliferate also does not use the word target in the rules text.
You cannot cast an Aura Enchantment on a creature with Shroud, because Aura spells always target.
You cannot use the Equip ability on a creature with Shroud, because the rules definition of Equip uses the word "target" (as you see in the reminder text for Equip).
Diffusion Sliver's ability only triggers when a Sliver is targeted; which Wrath of God does not do.
Phantasmal Image also only triggers when it is targeted, so it will not be affected by Nausea.
You can still choose an opponent with Shroud with abilities such as Stuffy Doll which tell you to “choose”, because choosing isn’t the same as targeting.
Sleep targets a player, not individual creatures. That means that creatures that player controls with Hexproof are still affected.  However, if the player themself has Hexproof, you cannot target that player.
Attached permanents are not protected by the Hexproof of the creature they are attached to, and can still be destroyed if a spell targets the attached permanent specifically (like Naturalize).  A card like Blastfire Bolt that targets the creature could not be used, though.

@ArcanistLupus I don't think it is that weird, or bizarre. Aura spells are targeted, but using another spell or ability to put an aura into the battlefield isn't an aura spell, so it's up to that specific spell or ability to determine whether it's targeted.

The target definition is rather spelled out but maybe having a bullet-point about choose a thing not being equivalent might be nice to have.

You can also vote for a permanent with Shroud during Council's Judgment.

"Aura spells are only targeted when they are cast" Minor gripe, but I believe Aura spells are always cast, I don't believe there is a way to copy permanent spells, which would be necessary for an aura spell to not be cast, as per 706.10. As such, the sentence could be something like "Auras require a target only when they are cast as a spell. If an aura enters [..]" etc.

One tricky loophole is when a card tells you to "choose" permanent types, like Tragic Arrogance does. You're not "targeting" the...subjects of the spell because the word "target" does not appear on the card, so you can still choose permanents that have hexproof or shroud.

@Hackworth The sentence is fine the way that it is because an Aura can enter the battlefield having not been cast. For example, Aminatou's -1 says "Exile target permanent you own, then return it to the battlefield under your control." (emphasis added).

Gendolkari's answer is excellent and answers the question quite thoroughly.  Here's a high level summary for people who want a more intuitive understanding:
Hexproof and shroud only stop spells/abilities that target.
Things that target:

Spells/abilities that say the word "target"
Auras
Spells/abilities that have the word "target" in their expanded text (like "equip")

Everything else doesn't target. Notable examples of things that don't target:

Spells/abilities that refer to "each" or "all" of something (such as Day of Judgement)
Spells/abilities that say to "chose" without saying "target" (such as proliferate)
Spells cast with overload (which replaces the word "target" with "each")

Targeting has nothing to do with how many things a spell/ability effects, but whether or not those things are literally targeted.  So spells with replicate/strive (such as Pyromatics) still target whereas spells cast with overload (such as Electrickery) don't.

Missed a close brace on Electrickery

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How does second edition farmer scoring work?
Related to this question; I am wondering how “each city can only be scored once” worked in the second edition rules. Second edition, like third (current); scores each farmland as opposed to scoring each city. But if a city can only count once; then how do you treat a city that is adjacent to multiple farms?
A simple example; imagine a competed game where there is only 1 city; and it has 2 farms touching it. Each player controls a different farm. In third edition, each farm would be worth 3 points. What happens in second edition?
I was able to find the rules for first and third editions online; but not second.

A city can be scored once per player, so in the given example, each player would receive 3 points.
I found the answer while combing through some threads on boardgamegeek.com, as well as in an answer to this other question.
From the other answer:

A player can score for a single city one time, and only one time... no matter how many fields and farmers he has next to it.

And from bgg:

German 2nd Ed:
  1) look at each city
  2) if a player has the most farmers in any one of the
  fields adjcent to the city he scores 3 points.

So it appears that while second edition does consider each field separately; it still scores city-by-city, as opposed to scoring farm-by-farm, and for each city multiple players might score the 3 points.

The answer to the previous question is wrong. The farm rule for the Rio Grande Games edition, which you are calling the second edition, is the same as the current farm rule. (Note, some people call the current basic game the second edition. I can find no evidence that any of Hans im Gluck, Rio Grande, or Z-Man Games number their editions.)
The confusion arises from the awkward way in which the Rio Grande rules were written. The writer doesn't seem to know if he's scoring farms, farmers or cities.
From Rio Grande Games Carcassonne
FARMER SCORING (for supplying the completed cities)
•Only completed cities are used for scoring farmers.
•The farmer must be in a farm that borders a city to supply it.
The distance of the farmer to the city is unimportant.
•For each city a farm supplies, the player who deployed the most
farmer(s) in the farm earns 3 points, regardless of the size of the
city. If players tie with the most farmers, each scores 3 points.
•A farm can supply (score) several cities if they border the farm.
•Several farms can supply a single city. In such a case, each farm is
scored separately, as descibed (sic) above.
When all completed cities are scored in this way, the scoring and the game is over.

The link does not work.

Works now, but it looks like that's a link to third edition rules. You can tell because a small (2-tile) city is worth 4 points instead of 2 points.

There must be more than three editions. The last time I checked a physical rule book, which was many years ago, it had the small city exception and scored farms as they are currently scored. That is, it was a combination of what people are calling the second edition and the third. It seems strange to me that no one has a copy of those 2nd edition rules.

There are certainly more than 3 printings; but I've never seen anything about a 4th version of the rules. From what I can tell, second edition was very similar to current edition farm scoring; but it didn't allow for a player to receive more than 3 points from a single city.

As far as finding a copy of the actual 2nd edition rules; I think that it was never printed in the US this way. The rule changes were made by Hans im Glück for the German printing, and Rio Grande only reluctantly adopted the newest rule later on.

I was looking through a Carcassonne thread on BGG. If every post is accepted as accurate, there were at least 6 combinations of farm and small city scoring.

Can you be more specific? Although I saw people wording the rules in their own ways, I never found more than 3 different versions of the rules mentioned.

Let us continue this discussion in chat.


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Why is Monstrosity not a keyword ability?
As pointed out recently in a comment on another question, Monstrosity is actually a keyword action, not a keyword ability. This seems strange, especially as it is the only keyword action that is not a verb.
Every card that uses monstrosity has it in the same format: An activated ability with a mana cost; where the only effect of the ability is the monstrosity.
Given this, it seems like it would make a lot more sense to have made monstrosity a keyword ability that has both a cost and modifier built into the definition; similar to the way Awaken, Suspend, and Reinforce work... instead of: 5RR: Monstrosity 3,
use Monstrosity 3 - 5RR..
The language just seems more natural, due to the fact that "monstrosity" isn't a verb. Is it known if there had been plans to have monstrosity be used in ways other than an activated ability? Having it as an action makes sense if there were other ways of it occurring, such as through a triggered ability (Whenever [this creature] attacks with at least 3 other creatures, Monstrosity 2), etc.
Looking for either a word from Wizards on why this choice was made; or something about the mechanic that I missed as to why it needs to be an action instead of an ability.

Because... they can
It sounds dumb.  But instead of asking why Monstrosity is a keyword action, ask instead why various keyword activated abilities aren't keyword actions, and it starts to become clear that all of them have some caveat that makes them less ideal as actions, and Monstrosity has none of those caveats.
Equip, Unearth, Level Up, Scavenge
These abilities can only be activated at sorcery speed.  If they were written as activated keyword actions, that restriction would have to be written into each ability, making them wordier (and creating the possibility that they could exist at instant speed, which was not the intent.)
Cycling, Transmute, Reinforce, Ninjutsu
These abilities all have an additional cost of discarding the card from your hand. (Except for Ninjutsu, where the additional cost is "Reveal this card from your hand, Return an unblocked attacking creature you control to its owner’s hand") Again, if this was an activated ability then that would have to be written into the text of every card, and that would imply that the discard cost was not an intrinsic part of the ability, which is inaccurate.
Embalm, Eternalize
These two fit in both of the above categories.  They're sorcery speed only, and they have an additional cost (in this case, exiling from the graveyard).
Forecast
Forecast is a bit weird because it has a totally variable activation effect.  I'm not sure why they chose to write the additional cost into the abilities rather than keeping it as reminder text, but it too has a timing restriction so even with the written out cost it still wants to be a keyword ability rather than an action.
(I probably would have templated Forecast as "Forecast {cost} / Whenever you forecast {cardname}, {do thing}" the way extra cycling riders work, but I suspect that that ends up being wordier when you add in reminder text)
Morph
I'm not going to even get into morph.  Its weird, and it's actually a static ability, not an activated one.
Monstrosity (and it's sequel, Adapt) have none of these problems.  There are no additional costs to the ability, it can be cast at instant speed, and there are no other riders or restrictions as to when the ability can be activated.  So they can make it a keyword action if they want to.
There are benefits to making it a keyword action if they can.
It makes it possible to make triggered Monstrosity effects in the future if they want.  It slightly reduces the amount of reminder text needed (from "{cost}: If this creature.." to "If this creature...").  It means the actual text of the card looks like the activated ability that it is.
That last item is probably the most significant.  A keyword ability with a cost provides no information as to how it works - it could be an activated ability, a triggered ability, or even (in the case of morph) a static ability.  By writing Monstrosity as an activated ability with a keyword action it provides that much more instant information about how it works for the player encountering it for the first time.

It is a lot easier to print a card like Nemesis of Mortals if Monstrosity is a keyword action rather than a keyword ability. For reference, its Monstrosity ability says this:

{7}{G}{G}: Monstrosity 5. This ability costs {1} less to activate for each creature card in your graveyard.

Keyword abilities almost never have those kinds of riders that aren't built in to the definition of the ability.

In addition, Monstrosity as an ability would have two different parameters: the number of counters to add and the cost. That is very rare in keyword abilities and the complexity that would introduce probably factors strongly into this design choice.
Among other keyword abilities with two parameters, Awaken and Suspend are not effects that can be expressed as keyword actions, and Reinforce is specifically an action that involves discarding the card, which would be lost if it was a keyword action.

Ghostfire Blade shows that Nemesis of Mortals would be totally possible, if slightly wordier (which is admittedly a significant concern considering how much text it already has).  I think the two parameter problem is the primary reason.

In regards to your second point, I gave the example of Awaken in my post; which has the same two parameters. That's where I got the format to use in my example with the dash.

Reinforce and Suspend also have this.

That's what I get for making a strong assertion without completely verifying it. I missed the mention of Awaken in the question and I forgot about the others.

Aeon Chronicler is an example of a suspend ability (suspend has a second parameter) with an additional rider.  "Suspend X—{X}{3}{U}. X can’t be 0."

Aeon Chronicler does have one simple and necessary rider on it's Suspend ability, but it's last ability is just a separate triggered ability. In this context, it's more similar to the "When this creature becomes monstrous..." abilities on some cards.

I believe it comes down to the level of control the player has over the effect. Just about every keyword ability* is an either an alternate cost, replacement effect, or triggered ability, passive effect, or else applies to the card when it is not a permanent. These are all things players either do with the card when it's not a permanent, or else have no direct control over. However, Monstrous is part of the creature permanent (not the card/spell as it's being cast) and is done only when the creature is on the battlefield.
Since players are meant to have control of their creature becoming monstrous, it should mimic other things that players have control over, such as Regenerate or Scry.
It's wording is a bit clunky (it makes sense 'to scry' or 'to regenerate', but not 'to monstrosity'), but this could have just been a shortcoming of English that there is no single very meaning 'to make monstrous'.
*Level up is the only keyword ability I could find that is activated when the card is a permanent. I assume this was done to save space on the card.

There are multiple keyword abilities that represent activated abilities on permanents: Equip, Outlast, Crew, and Level Up as mentioned in the answer.

Brevity, and lack of a better word (Probably)
I searched quite a bit for an official answer, but I can't find one.  That said, I came up with an answer and then noticed that Arcanist Lupus already alluded to this very briefly.  If you look at the cards with Monstrosity, they are extremely verbose cards that are approaching the maximum number of lines that could exist in the text box for the font size that was used.  For the reminder text of Keyword Abilities that are activated abilities (such as Equip or Cycling) the cost is repeated in the reminder text to remind players that the ability is in fact an activated ability.  Some examples of cards at the time that interacted with activated abilities were Pithing Needle and Oppressive Rays, so reminding players that the ability was activated was likely considered extremely important.
As far as the name being a noun, the billing of Theros was around the concept of heroes and monsters, and as heroes corresponded to Heroic, they wanted the monster mechanic to be a single word with a base of "monster" for symmetry.  I don't believe there is a real single word that means "to become monstrous," but one was invented on the card Monstrify.  My guess is that they didn't like that because it is a fictional, silly-sounding word and because it was already a name of an existing card which is unrelated to the Keyword Action.

There are 135 Keyword Abilities.
Of all those only two are activated abilities of creature cards that function on the battlefield.
Level Up - part of a weird highly non-standard card template.
Outlast - post-dates Monstrosity, requires an empty stack in the main phase.
Every other keyword ability for creatures is static, triggered, or functions in a zone other than the battlefield.  So the weight of data suggests that R&D is quite biased towards templating things that function as an ordinary creature's activated ability as activated abilities for whatever reasons they have that don't seem to be stated in any blog posts (simply familiarity for players?).  (e.g., why was a keyword ability 'Ping 1 - {T}' never created for Pyromancers back when they first went keyword-happy post 6th-ed?)
Players have been conditioned to think 'Monstrosity 5 - {5}{G}{G}' would be far more likely to mean something like 'As you cast this card you may pay an additional .. and it enters ..' or 'When this creature deals combat damage if it is not monstrous you may pay ...' than to be an 'ordinary' activated ability.
Outlast really seems like the oddball (noting that Adapt post-dates both and returned to being a keyword action, not a keyword ability).

I don't remember hearing anything about this mechanic specifically, but Mark Rosewater defines keyword and ability word in DtW #81 (Theros pt 2).

If you take the ability word off the card, it just works. The ability word doesn’t do anything to make the card work, it’s just a way to group it thematically.
But a keyword is something in which it needs to be on the card. Now, you can’t reference ability words, but you can reference keywords. So for example, if I wanted things to reference this ability, I needed it to be a keyword and not an ability word because ability words can’t be referenced.

There are quite a few cards which check to see if a creature is monstrous.  Therefore, in order to check if a card is monstrous, monstrosity must be a keyword, not an ability word!

I think you misunderstood my question; I was not asking why it's not an ability word; but rather why it is a keyword action rather than a keyword ability. (Keyword ability being a distinct thing from ability word).

In addition, checking whether a creature is monstrous doesn't actually reference the keyword. It references a named effect created by the keyword. They could write "this creature becomes monstrous" in a Landfall ability and those checks would see it.


text:
What happens if a creature has no toughness defined?
Dominaria introduced Merfolk Trickster, which causes a creature to lose all abilities, without setting a power and toughness.
What happens if a card such as Tarmogoyf loses all abilities?
Would Tarmagoyf become a 0/0 in this case, because a number not defined is treated as 0? Or would it possibly be a 0/1, because the printed toughness on the card is "*+1", and only the "*" part is undefined? What about a card like Boneyard Wurm, would it just become 0/0 (and thus die)?
There seems to be a possible contradiction between the comprehensive rules and the Gatherer rulings. The Gatherer rulings say:

If the target creature has power and toughness written as / with an ability that defines its power and toughness, it’s 0/0 when it loses all abilities. If its power and toughness are written as */*+1, it’s 0/1, and so on.

Rule 208.5 deals with this situation:

208.5. If a creature somehow has no value for its power, its power is 0. The same is true for toughness.

It seems to me that a Tarmagoyf that loses all abilities has no toughness defined. It's toughness is written as "*/1+*", which according to 208.2, its toughness should be defined by its abilities.
So, while it is clear that a */* creature will be a 0/0 if it loses all abilities; what happens to a */*+1? Is it 0/0 or 0/1?
Also, I find it interesting, though not likely relevant, that Tarmogoyf is written "*/1+*" (with the 1 first), while the Gatherer ruling references cards that are "*/*+1" (with the * first).

I have updated this question in response to Merfolk Trickster, and unaccepted the accepted answer; which may or may not still be correct.

With the introduction of Vehicles in the set Kaladesh, this situation is now possible and explicitly covered by the rules.

208.5 If a creature somehow has no value for its power, its power is 0. The same is true for toughness.

Neat! Can you provide an example of how a vehicle might have no power or toughness defined?

There's a question about it here: https://boardgames.stackexchange.com/questions/33497/how-on-earth-do-i-crew-a-non-vehicle; short version is you give a vehicle's Crew ability to something that's not a vehicle or creature.

This question is hypothetical and not covered by the rules. All current cards which cause a creature to lose all abilities also set the power/toughness of the creature, or cause it to no longer be a creature making the power/toughness irrelevant.
It's a safe bet that  loses all abilities cards are designed that way to avoid this conundrum.

It's not clear from that rules quote that this is correct. "If the ability needs to use a number that can’t be determined, use 0..." But this isn't a case of the ability not being able to determine the number. In this case, the ability doesn't exist.

@ghoppe I think we all agree that you can't determine the value of the asterisk. But with the ability removed, 208.2a can't apply - there's no ability for it to apply to - so it seems that there's nothing here to determine what the asterisk means. So is there another rule that explains how to determine the value of a placeholder like the asterisk when there's no ability?

@Jefromi Yes it took me a minute to consider the argument, and I agree. I've changed my answer.

@Jefromi It is interesting that 208.2a and 208.2b both say that the creature "may" have an ability that sets the stats, but no mention of what to do when they don't have that ability. I think their intent was to say that such a creature will either have one or the other at all times.

I'm not super good at old cards, and I don't know how to search on Gatherer for an asterisk in power/toughness - were there any of those guys early on? I'm sure the current rules were written with the knowledge that this can't happen, but I'm not as sure about the early lose-abilities card designs. (Humility isn't exactly a poster child for avoiding nasty rules interactions...)

@Jefromi Yes, old-timers will remember Nightmare from Alpha. These cards have always been in the game. It's likely because of Nightmare that loses all abilities cards are designed the way they are.

@ghoppe Ah, that's the name, thanks! I thought there was something old and black and scary, and somehow couldn't come up with it, despite the recent reprints.

Sudden Spoiling is not caught by that search due to a 1-letter difference.  And Lignify says "with no abilities".  There may be others that also use slightly different wording

This is objectively a worse answer than the one by Michael Snook.

@SoldierofVol Which isn't surprising considering Michael Snook answered the question two years after I did, after the rules changed and explicitly covered the situation. ;-)

You can always update this answer to include more accurate information.

This is no longer true with Ray of frost also, the alchemy card Patriar's humiliation that doesn't have the color restriction

Tarmogoyf will be a 0/1 in this case.
As long as Tarmogoyf is missing its characteristic defining ability, the only information available for determining its power and toughness are the */*+1 printed on the card. So, it's not exactly accurate to say that it has no value for it's power, but rather, it has a value determined by an undefined symbol, and a calculation involving that symbol. In that case, rule 107.2 applies:

If anything needs to use a number that can’t be determined, either as a result or in a calculation, it uses 0 instead.

Since the start symbol has a value that can't be determined, the Tarmogoyf's power and toughness are evaluated as 0/1+0, or 0/1.
Similarly, Boneyard Wurm's power and toughness is printed as */*, which would evaluate to 0/0 while it has no abilities.

So, you're saying a */* creature like Nightmare would have 0 toughness and die?

Yes, that is what I'm saying. I added a bit covering that in my answer.

There have been no printed cards that remove static abilities without also setting the power and toughness (Snakeform, Ovinize) or changing the card to no longer be a creature (Soul Sculptor) as stated in ghoppe's answer.
Tarmogoyf's ability which sets its power and toughness is in a special class of static abilities called characteristic-defining abilities [CR 604.3] which function in all zones and even outside of the game. Any hypothetical card which exclusively removed static abilities would need a special ruling on its interaction with these type of abilities.
Asterisks * representing power and/or toughness are treated as 0 (even within calculations) in the case of static abilities that create replacement effects [208.2b] and also characteristic defining abilities when the value of the asterisk cannot be determined.
In addition to these definitions, Gatherer also treats asterisks as zeros with constants added continuing to be added. To find Tarmogoyf in Gatherer by Power and Toughness alone, one must set the search parameters to Power=0 and Toughness=1.
It is reasonable to assume that any future ruling would be consistent with this and set completely undefined asterisks to zero, although this is just speculation on my part.
If we assume that the above proves true then we can make the following conclusions regarding the specific creatures mentioned in the question.
 - If Tarmogoyf somehow lost his ability which defines the value of *,
   then each * would be taken as equal to 0 so that it would become
   0 / 1+0 => 0/1.
 - Boneyard Wurm would become a 0/0 and thus under [CR 704.5f], be put
   into its owners graveyard. (Of course, once in the graveyard its power and toughness would be reset based on its characteristic-defining ability)
The rulings for Nightmare help clarify some of the interactions with asterisks in power/toughness.

If you control 0 swamps, then the Nightmare has 0 toughness and will be put into its owner's graveyard as a state-based action right before the next player gains priority.
Nightmare's power and toughness changes as the number of Swamps you control changes.
The ability that defines Nightmare’s power and toughness works everywhere, not just on the battlefield.

EDIT
[CR 208.2a] in reference to Asterisks in Power and Toughness

This ability functions everywhere, even outside the game. If the ability needs to use a number that can’t be determined, including inside a calculation, use 0 instead of that number.
Example: Lost Order of Jarkeld has power and toughness each equal to 1+*. It has the abilities “As Lost Order of Jarkeld enters the battlefield, choose an opponent” and “Lost Order of Jarkeld’s power and toughness are each equal to 1 plus the number of creatures the chosen player controls.” While Lost Order of Jarkeld isn’t on the battlefield, there won’t be a chosen player. Its power and toughness will each be equal to 1 plus 0, so it’s 1/1.

It's not clear if the undefined quantity that would become zero would be * or *+1, since the rules don't explain anywhere what we must do if a sum appears where the thoughness should be. That's why it is unclear if Tarmogoyf would be a 0/0 or a 0/1. That's why this situation is currently not covered by the rules.

"Asterisks * representing power and/or toughness are treated as 0 (even within calculations) when the value of the asterisk cannot be determined." Can you find a rule for this? I don't think there is one.

I guess I should have quoted the one rule that was under most contention. The comprehensive rules are very clear that what I said is correct. I will post the example within the CR that further explains the asterisk rule.

@JRaccoon The rule you've quoted was discussed on the other question too. The issue is that the rule is explaining how the ability containing the asterisk works. But we're talking about a situation where the ability has been removed. 208.2a is talking about how a certain kind of ability functions... but now there is no such ability, so 208.2a doesn't apply any more than it applies to your Grizzly Bears that never had an ability like that in the first place.

@JRaccoon Now, if there actually were cards that removed abilities without setting power/toughness, I'm sure that they would fix the rules such that the asterisk was 0 as you've said, and it wouldn't be a hard fix to make. But the rules as written don't actually say "here's how you figure out what value an asterisk has". They talk about how the ability works.

@Jefromi Of course, as there are no rules that explicitly remove these static abilities, we can't say for sure what the official ruling would be. Based on the wording of all related rules, if a card that removed static abilities was printed with no changes to the rules, a judge would have no choice but to rule that the asterisk represented a 0 while any constants added to it remained.

Exactly. The comp rules as written are not clear that  this is correct. I'm sure you're right that a judge would rule in this way in a hypothetical scenario, or if they needed to fix this gap in the rules they'd fix it this way, but it's really misleading to claim that they actually say so already.

I said "Any hypothetical card which exclusively removed static abilities would need a special ruling on its interaction with these type of abilities." I don't see how that is promoting anything not explicitly in the rules. I edited my post to include the rule asked by Gendolkari in the comments, which is correct and directly quoted. The examples of Tarmogoyf and Boneyard Wurm were just to illustrate how when the value asterisks change, the card is subject to being sent to the graveyard when its toughness reaches zero and when the asterisk is zero, other constants are added to it.

Yes, you said new rulings would be needed, but then you go on to say "If Tarmogoyf somehow lost his ability which defines the value of *, then each * would be taken as equal to 0 so that it would become 0 / 1+0 => 0/1." You don't say "this is hypothetical, how I think it should/could work", you present it as fact. It sounds like you actually agree with everything that was said in the top answer (and in the comments to it) and you're trying to present some more detail, but you're doing so in a misleading way.

let us continue this discussion in chat

This is no longer true with Ray of frost also,the alchemy card Patriar's humiliation that doesn't have the color restriction

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What happens if both players have the ability to pump their creature an unlimited number of times?
Say that both players each had 2 Leaden Myr, 2 Myr Galvanizer, and a Nantuko Shade. (Or any other way to get unlimited mana, and a Nantuko Shade).
Player 1 attacks with his Nantuko Shade, and player 2 blocks with his Nantuko Shade. Before damage is assigned, each has chances to pump up their Nantuko Shade as much as they want. They can't just declare them to be "infinite," but each can always one-up the other player. What happens?
It seems there would be a loop of events, but would one player eventually be forced to break the loop as per rule 714.3? Is it considered the same game state after each player pumps their creature a bunch as it was before?
This was discussed at length on the Draw3Cards Magic Q&A site (which is no longer available), but no conclusion was reached. Some felt that the game would simply be a draw, others felt that the active player would be forced to make a different decision to break the loop. Others felt that you would just have to call a judge and see what he decides.

This is a fragmented loop.  The active player (whose turn it is) would be forced to make a decision that stops the loop.

719.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.
Example: In a two-player game, the active player controls a creature with the ability “{0}: [This creature] gains flying,” the nonactive player controls a permanent with the ability “{0}: Target creature loses flying,” and nothing in the game cares how many times an ability has been activated. Say the active player activates his creature’s ability, it resolves, then the nonactive player activates her permanent’s ability targeting that creature, and it resolves. This returns the game to a game state it was at before. The active player must make a different game choice (in other words, anything other than activating that creature’s ability again). The creature doesn’t have flying. Note that the nonactive player could have prevented the fragmented loop simply by not activating her permanent’s ability, in which case the creature would have had flying. The nonactive player always has the final choice and is therefore able to determine whether the creature has flying.

In essence - the attacking player is screwed.

I'm not sure this is actually applicable here - specifically, the same game state is not being reached (as the power/toughness of the relevant creatures has changed).  It's not clear to me that the rules actually handle this situation cleanly, though I presume the resolution would look something like this.

It sure sounds like the same thing to me but in this case it is cycling if just the defending creature dies or if they both die.

@JoeW The problem is that while 'Game State' doesn't actually have a formal definition within the comprehensive rules (!), it surely must include things like the power/toughness of creatures.  For instance, imagine a card that read 'creatures with power greater than 100 have Trample'.  This card wants to know exactly what the P/T of every creature in play is, and so pumping a creature must yield a distinct game state.

If both players pump up their creature by the same amount each and every time then what else can you call but a fragmented loop? If both creatures are 1/1 or 100/100 the results are still the same.

I'm not saying that 'fragmented loop' doesn't define the concept; I'm saying that the rule specifically speaks to 'the same game state being reached multiple times' and having a different P/T on a creature than previously seems clearly to be a different game state.  Their example even calls this out, where the result after a loop is explicitly the same (nothing about the game is different, other than 'an ability has been activated').

I assure you, as the attacker if you have Backlash or Fling in your hand, when both creatures change from 1/1 to 100/100 the results are not the same.

If power/toughness were no part of the game state (which I don't believe to be true), both the AP and the NAP can do something else to change the game state, like tapping a land, casting a spell. That way, game state is changed and they're both ready for another round of pumping. As that would still leave the AP at a disadvantage, the AP has to hope that the NAP has pumped their Shade to just one more than the AP's Shade, and then cast (for instance) a Giant Growth. That way, the NAP has to respond by pumping and the AP can now respond by pumping.

Both players can only pump their shade +1/+1 per loop of using their Myr. This means they can each apply one pump, then they need to wait for the stack to empty to untap their Myr. Then they can repeat this. In this way no player can pump their Shade using the loop more times than the other player, since each time the stack resolves each player can pump their shade once. Surely this means that the Shades would always be in sync, modulo number of swamps? And therefore the loop the players agree to shortcut will always boost both shades the same amount +the number of swamps?

If I were the judge called over, I would rule both shades to be destroyed. One end to a loop like this is that there is one infinity/infinity creature blocking another. Unless either player has some trick to get one of the shades out of combat, destroy the other, or do something else that would affect the loops infinite outcome, then they both should be destroyed.

@user1873 Okay but that would be breaking the loop if they played something else. The point is as long as it is just players taking turns pumping their creature +1/+1 then nothing changes and you have a pointless loop.

@JoeW," just players pumping their creatures +1/+1 then nothing changes" Nothing except the P/T of the creatures, so I don't think you can claim that you have the same game state.

@user1873 If One creature attacks with a power of 1/1 and another creature blocks with a power of 1/1 and they both get pumped up to 100/100 or 1,000/1,000 or 1,000,000/1,000,000 has anything really changed other then the numbers got larger? Both creatures are still going to die and that is it.

@JoeW, I think the problem is that WotC has never defined game-state. but without an official definition of game state it is difficult to answer.

Game state 1 one has attacking and defending creatures with equal power and toughness and both dying. Game State 2 (after attacker pumps up creature) has the attacking creature up by +1/+1 and living. Game State 3 (after the defender pumps up the creature) has the both creatures with equal power and toughness and dying and is the same as Game state 1 and the same for Game states 4+. Any way you look at it you just get a toggling of state with the attacker living or dying based on who acted last. How is that different then the example of the creature gaining and losing flying?

I think the cited rule does give a subtle hint as to what constitutes game state: and nothing in the game cares how many times an ability has been activated, so as long as nothing in the game currently cares about how large a creature is, the rule should apply here.

@Hackworth, but there is the rub. Both the blocking and attacking creature care what the other's P/T are, since knowing that determines which creature if any dies/lives. Given the CR example, what if one plyer controlled a creature thats P/T was altered by the number of creatures with flying in play? (Then woul nothing care about the flying status of the {0} activation creature?

@Hackworth: Actually that distinction is designed to simplify the example, not exclude other cases. The active player is allowed to say how many times the thing happens if the number of activations matter. For instance "I do this 100 times if you are going to do it every time I do". By removing anything that cares, the rules can avoid the counting concept neatly (which is really asymptotic to 716.3, since it is just about how to break the loop, not what happens as a result of the loop).

@user1873 If both the attacking and defending creatures have the same power/toughness it doesn't matter if its 1/1 or 1,000,000/1,000,000. The results will be the same for both creatures and all the endless loop does is waste time.

So we can agree that IF it constitutes the same game-state after both creatures get larger, then the Active Player is forced to end the loop and not pump his creature. But IF it is indeed a different game-state, is there any rule at all that deals with that? Would it be a forced draw?

@GendoIkari: Personally I do not believe it is possible. There does not exist any sequence of actions that can be repeated without encountering some semblance of "repeated game-state" thus triggering 716.3. For instance a judge recently ruled that an Eggs deck is not allowed to repeatedly put everything into the graveyard and shuffle, since it is creating a repeated game-state. (I can't find a reference unfortunately)

Ok, folks - I appreciate the passion here but I believe this thread has gone on long enough.  Please cast your votes or enter a new answer if you believe another viewpoint needs to be heard.  Thanks!

I would like to make the case for "Nothing happens. Both creatures will die as 1/1 or 2/2." in this special case. I think this would happen due to how the stack works.
Let's say Alice decides to start the pumping process. She taps both Leaden Myrs to get two black Mana, spends one to pump her Shade and the other to activate the untap ability of one of her Galvanizers. Bob does the same in response. Now we have two 2/2 Shades posed to fight each other and one tapped Galvanizer on both sides.
After Galvanizer's ability resolves, Alice receives priority. She taps a Myr for a third black mana and then uses it to activate the untap ability of her second Galvanizer. Bob decides to seize the opportunity and activates his second Galvanizer's ability in response. It goes to the top of the stack and since Alice has nothing to respond herself (aside from maybe giving the Shade one further +1/+1), it resolves first. Now Bob's Myrs untap and Alice's untap ability is still on the stack. Bob won't let that ability resolve until he has used the combo to +10/+10 his Shade.
Now Alice can try to pump her Shade as often as she wants, but Bob will always respond with +10/+10 for every +1/+1 she can muster. So, Bob informs her that he will respond this way every time and asks Alice how often she wants to pump her Shade. Whatever she says, her Shade will be weaker and thus die.
Conversely, if Alice passes priority without doing anything, and Bob starts to pump his Shade, Alice will be able to always respond with a +10/+10 for each of Bob's +1/+1. Then, Bob's Shade will die.
Knowing this, Alice will pass priority, as will Bob, without doing anything and both Shades die as 1/1.

Where did Alice get the third mana to activate Galvanizer in the first sentence of the third paragraph? She got two black mana, and then used one to pump the shade and one to activate the first Galvanizer. Then she uses another to activate the second Galvanizer.

@Rainbolt: Both her Myrs untapped due to the untap ability of the first Galvanizer resolving. She uses one of those to produce the third black mana.

That makes sense. This answer is brilliant by the way. You went beyond the rules and actually thought about the problem. Nice work!

Thanks for the edit! Reading it back, I still found some occurrences of "his" when talking about Alice's permanents. That happens when you decide giving "One player" and "the other player" names halfway through the process of answering.

While you get my upvote because I think this answer is potentially useful for someone reading this, it doesn't really answer the question. It's a possible way the players can act, but in the scenario given by the questioner, that's not the way they choose to act (otherwise, this question wouldn't arise). In a tournament scenario, it would be a very bad idea of the judge (or any other outside person) to hint the players of a specific course of action, so while witty, this is not the solution.

I don't think this holds up. Alice could tell Bob that she's going to pump her Shade every time Bob passes her priority as long as hers is weaker, and ask Bob how long he wants to keep one-upping her. I don't see anything in the rules that lets one player force the other to make the unfavorable choice.

This answer is based on a misconception of how infinite sums work... An infinite number of $1 bills and an infinite number of $20 bills would be worth the same. As explained in this video --> https://www.youtube.com/watch?v=M4f_D17zIBw

Rule 716.3 does not apply because there is not a point after any group of independent actions, or recognized shortcut, where the game state is the same as a previous game state. Every time the exercise is preformed, the Nantuko Shade power and toughness are increased by +1/+1 or black mana has been added to a players mana pool.
From that, each players could define a shortcut where they pump their Nantuko Shade at least once more than his or her opponent.
Failing the existence of an card or effect, external to these five creatures in play, that could be used to remove or disable one of them, the actions can continue unabated until one player freely decides to not pump his or her Nantuko Shade.
The further contention arises from the result of this chain of events on tournament play. Since game state changes, and each player has an interest in winning the conflict, it would be hard to call this slow play. Since it happens in the course of combat, the game won't end by going to turns. In the end, one player will have to agree to pump his Nantuko Shade less than his opponent, on the assumption that they can win the game through other means still in their deck, and that is preferential to having the match end in a draw.

Look at the definition of slow play, it includes "Players must maintain a pace to allow the match to be finished in the announced time limit." Attempting to one up forever is the definition of not allowing the match to finish in the announced time limit. You are thinking of the quote "It is also slow play to..." (emphasis mine) which references loops where you don't know how long it will take.

@Guvante - Thus the dilemma, and my conclusion regarding a player's decision to not pump further. The pace is constant, each player is just responding to the actions of the other.

This situation used to be covered in a different way by the Comprehensive rules. According to this Mark Rosewater article, the following rule existed in 2002.

421.5. If the loop contains at least one optional action controlled by each player and these actions don’t depend on one another, the active player chooses a number. The nonactive player can either agree to that number or choose a higher number. Note that this rule applies even if the actions could exist in separate loops rather than in a single loop.

So this situation could be handled by Player A saying "I propose that we both pump the Nuntako Shades to 9000/9000". Player B either accepts that number, or proposes a higher number. (That higher number would be final.)
Now the loop "sequence" rules have been rewritten.

719.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a nonrepetitive
  series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can’t include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this
  sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.

So the player with priority proposes the shortcut. "I propose that our shades are pumped to 9000/9000 and then you have priority." Note that they could propose that they have priority. (Perhaps to threaten a trick?)
Next Player B has a decision:

719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence.

So Player B can either say "Stop the loop when our Nuntakos reach 8000/8000" (and they must make a different decision that will break the loop) or "I accept that proposal, I get priority when our Nuntako's reach 9000/9000 and the loop ends."
Note that this situation contains 3 loops (or 4 depending on how you define it). Loop A: Player A pumps their shade an arbitrary number of times, Loop B: Player B pumps their shade an arbitrary number of times, and Loop C: priority is passed an arbitrary number of times.
719.2a states "This sequence may be a nonrepetitive
series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns."
So theoretically player A could propose a shortcut like "I will hold priority while pumping my creature by 10, pass priority and you pump yours by 10, until both creatures are 90/90" for whatever reason.
IN SHORT: The active player proposes a shortcut which defines the number of times loop(s) are repeated and the ending game state, the other player may then accept this shortcut, or shorten the loop(s) at some other arbitrary point and make a different game choice that doesn't result in the same loop(s).
Result: Both Nuntakos will die at X/X power/toughness where X is chosen by the active player, unless the non-active player can make a decision (a card or ability to play) and chooses to break the loop earlier.

How is a former version of that rule relevant at all? I'm wondering about this specifically because that seems to be the only unique part to your answer, seeing as the rest answers what would happen if players agreed to have both Shades at the same power level (which, the way I understand the question, is not the case).

The game doesn't end in a draw
This is true in any case, and I haven't seen it mentioned in here before. Here's the rule for games ending because of a loop of actions:

104.4b. If a game (...) somehow enters a "loop" of mandatory actions, repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don’t result in a draw.

Since nothing about this interaction is mandatory, there's no way this would end in a draw.
This situation isn't a fragmented loop
Note: The following rule's number used to be 716.3, which is widely referenced in other answers

719.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached (...)

The rules don't give a specific definition for "game state", but the only possible interpretation without breaking the rules is that it includes all information required to reconstruct the game from scratch, should you attempt to do so. Static buffs would have to be part of the game state, just like counters or whether a creature is tapped or not, or even on the battlefield. A 1/1 is simply not the same as a 1/1 that has +10/+10 - if you disagree, imagine the same game state with a Elesh Norn, Grand Cenobite in play for only one of the players. Game state should not be confused with relative board presence.
Further, the IPG mentions "triggered abilities that affects the game state in non-visible ways", which precisely applies to static buffs and granted abilities such as Flying in the example of 719.3.
Due to the game state changing after each execution of the loop, 719.3 doesn't apply.
How this plays out (in a tournament scenario)
From what's stated in the question, it would simply result in two equally sized Nantuko Shades at any point that would kill each other.
Assuming the players wouldn't be satisfied with that, they would call a Judge. As I stated in a comment to M.Herzkamp's answer, it's not the Judge's job to come up with other possibilities to what could have been done (and in fact should refrain from doing so, or at least telling the players about it), but to handle the presented situation. Now, there's a number of ways in which this could be presented (and keep in mind that the Judge's responses are what I deem to be applicable, and that actual Judge calls may differ in result):

The active player is complaining that every time they activate their Nantuko Shade's ability, their opponent does the same. This has been going on for a while.
This sounds like a perfect example of Slow Play (for both players), and might result in a Warning, or at least a remark about it.
The active player has proposed a shortcut of pumping his Nantuko Shade a set number of times with the combo described in the question, and the opponent agreed, however adding that each time the active player would activate it, they would activate their own Nantuko Shade in response.
All the judge can reasonably do here is confirm that everything's done by the rules, and that the shortcut proposed is legal, even knowing that after it's handled, situation 1 would likely occur, unless a player comes up with one of the different ways to play this scenario.

In other words, this might result in some Slow Play warnings, however if no player figures out a way to break the cycle, will likely result in equally proportioned Nantuko Shades that will kill each other.

I would also like to highlight something that the user Pow-Ian suggested this in the comments above:

If I were the judge called over, I would rule both [Nantuko Shades] to be destroyed. One end to a loop like this is that there is one infinity/infinity creature blocking another. Unless either player has some trick to get one of the shades out of combat, destroy the other, or do something else that would affect the loops infinite outcome, then they both should be destroyed.

This would be very harmful for the game in progress, and very much outside of the job description of a Judge. The comment suggests that you take control out of the player's hands by deciding how they will act (pumping the creatures to the same level) as opposed to judging what effects their actions have. Furthermore, you advance the game to the combat damage step by ruling that both creatures get destroyed, preventing both players from casting additional spells or activating abilities. Furthermore, you suggest to only do this if they don't have a means to break this non-mandatory loop, which allows for the interpretation of forcing them to cast a spell in their hand that they may cast or revealing the existance of such, even though the player never intended to do so. On top of that, suggesting to the players that "infinite" P/T exists is one of the less recommendable actions in this situation.
How this plays out in any non-tournament scenario
Without the problem/feature of Slow Play issues, and without the prohibited outside assistance, players are more likely to figure out a different solution, such as the one proposed by M.Herzkamp, and continue the game from that point. They might also just eventually put both Nantuko Shades in their graveyards, or agree on a draw, or yell at each other and never formally finish the game...

There is actually a question somewhere on this site that asks for a definition of "game state". I would link to it if I weren't on my phone. If you find it, you might be able to find evidence that your interpretation of the fragmented loop rule is correct (or not).

@Rainbolt: You might be talking about this one, which - while supporting my reasoning - is more exhaustive than needed, plus it has the downside of also being an opinion, despite being the "accepted" answer (and it's a good answer, don't get me wrong). For those reasons, I decided to include my own definition.

First things first, this is a fragmented loop as defined by 716.3, the definition of pertinent game-state is left up to the discretion of the players or the judge if involved. There is plenty of precedence that repeated usage of abilities that make a minor adjustment to the game state are considered loops. Since we have a loop we by extension have a fragmented loop due to having multiple players.
Unfortunately no one is talking about the shortcut employed by the players, which is very important to how the problem gets resolved.
In these instances a shortcut is not allowed unless agreed between players or a few actions have been taken to establish how the loop will function. How the loop begins drastically changes how the overall game will be impacted.
Assuming there are no other pertinent abilities available, it would begin with the active player having the option to activate an ability on the declare blockers step.
If they choose to begin creating mana, the non-active player can bury their loop creating a non-fragmented loop, allowing "infinite pump", similarly every time the active player tried to pump they could repeat that action. An example shortcut is "every time you pump I pump 100 times", since the active player is required to break the loop, this would end with their shade dead.
If they choose to pass, the non-active player would be given the chance. The reverse of the first example would happen. Note that in this case the active player has to break the loop, however since they got to pump before the loop started, this isn't a problem. The non-active player gets an extra pump, but that doesn't matter when the active player already got lots of pumps.
If the non-active player also passes then the two 1/1's kill each other.
Thus unless I am missing something, it is a game of chicken and thus will result in two 1/1's killing each other.
EDIT:
There is one other possibility that I didn't consider. If players aren't playing perfectly (as I described here) then the judge would walk the players through moving the game forward, forcing a "number of attempts" like in 716.3. Unfortunately without a lot more detail, including knowing how the players react to this walk through, it is impossible to tell ahead of time how that will be resolved.
I have heard of something revolving around choosing numbers with restrictions but don't know offhand what it was.
However this feels a bit contrived as tournament players being nice would be odd, since the benefits of not waiting are obvious at that level of play. Similarly at kitchen table I would expect players to just let both die as a compromise.

Any explanation for the downvote?

I din't downvote, but here is a possible reason someone else did. This isn't a fragmented loop; the game state changes each time the Nantuko Shade is pumped.

@DrunkCynic: You can disagree if you like but there is no meaningful way for a player with an iteration on the stack to ever pump their creature bigger than the other, since their actions are futile looking holistically it would be considered slow play to keep trying. I will note what happens with an empty stack.

Counter: Every time you pump I react by pumping.

Short Answer: The active player proposes a number of times they go back and forth doing this, and the non-active player either accepts it or proposes a larger number. (This is a change from what I wrote previously; the "on-high" ruling on this has to be adjusted to the new shortcut rules.)
Either way, they're going to wind up balancing out 1-for-1, equal number of pumps unless one of them voluntarily does fewer than their opponent.
Current Comp Rules:

719.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a “loop”). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.
719.2. Taking a shortcut follows the following procedure.
719.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can’t include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.
  Example: A player controls a creature enchanted by Presence of Gond, which grants the creature the ability “{T}: Create a 1/1 green Elf Warrior creature token,” and another player controls Intruder Alarm, which reads, in part, “Whenever a creature enters the battlefield, untap all creatures.” When the player has priority, he or she may suggest “I’ll create a million tokens,” indicating the sequence of activating the creature’s ability, all players passing priority, letting the creature’s ability resolve and create a token (which causes Intruder Alarm’s ability to trigger), Intruder Alarm’s controller putting that triggered ability on the stack, all players passing priority, Intruder Alarm’s triggered ability resolving, all players passing priority until the player proposing the shortcut has priority, and repeating that sequence 999,999 more times, ending just after the last token-creating ability resolves.
719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence.
  Example: The active player draws a card during her draw step, then says, “Go.” The nonactive player is holding Into the Fray (an instant that says “Target creature attacks this turn if able”) and says, “I’d like to cast a spell during your beginning of combat step.” The current proposed shortcut is that all players pass priority at all opportunities during the turn until the nonactive player has priority during the beginning of combat step.
719.2c Once the last player has either accepted or shortened the shortcut proposal, the shortcut is taken. The game advances to the last proposed ending point, with all game choices contained in the shortcut proposal having been taken. If the shortcut was shortened from the original proposal, the player who now has priority must make a different game choice than what was originally proposed for that player.
719.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.
  Example: In a two-player game, the active player controls a creature with the ability “{0}: [This creature] gains flying,” the nonactive player controls a permanent with the ability “{0}: Target creature loses flying,” and nothing in the game cares how many times an ability has been activated. Say the active player activates his creature’s ability, it resolves, then the nonactive player activates her permanent’s ability targeting that creature, and it resolves. This returns the game to a game state it was at before. The active player must make a different game choice (in other words, anything other than activating that creature’s ability again). The creature doesn’t have flying. Note that the nonactive player could have prevented the fragmented loop simply by not activating her permanent’s ability, in which case the creature would have had flying. The nonactive player always has the final choice and is therefore able to determine whether the creature has flying.

Full Explanation:
Case 1) Player A(ctive) is reasonable and suggests that they pump 1 for 1, and proposes a finite number N, responding to each other in turn and then stopping at that number. Player B is also reasonable and accepts. The game moves forward after each creature gets pumped that many times.
Case 2) Player A as above, Player B says a different number M, smaller (he changes the sequence at that point, but his only option to change it is to not pump his own creature). Result: A will pump +N, B will pump +M. Not optimal for B in most cases, so this will almost never happen.
Case 3) Player A as above, Player B says that after that shortcut, he wants to pump another P times. A will of course respond to those, forming a new suggested shortcut, the end result will be (eliding shortcut negotiation) P+N pumps to both creatures. (If A chooses not to respond in kind, A will have a smaller pump, again, rarely happens.)
Case 4) Player A suggests a shortcut that has only themselves pumping, but B will not accept the shortcut, because they will interrupt after the first by pumping, geting us back into Case 1.
Case 5) Neither player understands or accepts the simple shortcut of even pumping, and so they try to go back and forth forever. Slow play warning and explanation of why they are stuck with Case 1.
So, short answer: Player A names a number. Player B accepts or names a bigger number, and they both get pumped that many times. If player B wants to pump less, they can stop A's shortcut early, but this will only happen if B has a rare trick.

This doesn't explain anything, especially in comparison to the existing answers. At the very least cite the rules you have give the "short version" of.

Actually, it does explain what the result is. It does not, as you note, cite the comp rules involved, because as I noted, this was the current way of handling it when I was still judging and I have not dredged through the Comp Rules to find the current way it's expressed. Additionally, it wasn't a Comp Rule specifically, it was the "from on high" ruling about this specific situation, and they used a mish-mash of then-current comp rules to justify it. It was the "correct" way to do things for 10+ years, consistently used at PTQs to the Pro Tour.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
If a sorcery card gives -X/-X to a 1/1 creature till end of turn does the creature die?

I use Urge to Feed (-3/-3 until end of turn) against a 1/1 creature, does that creature die?
If I use Zealous Persecution in a multiple player game, would it destroy all 1/1 creatures on the battlefield except mine?
If I use Dead Weight to enchant a 1/1 creature, would it destroy that creature?

I am confused with the first 2 because it says "Until end of turn", so would the 1/1 creature go back to normal after my turn?
For the 3rd one, if it does destroy the creature then would the creature come back to life if the enchant is destroyed?

The creatures die in all of those cases. If a creature's toughness is reduced to zero (or less), it is immediately put into the graveyard. It doesn't matter if at the end of the turn its toughness would become positive again; it died long before then. There's no coming back from the dead (not without playing a card like Unburial Rites, anyway). In the third case, when the creature dies, since Dead Weight no longer has a creature to enchant, it also immediately goes to the graveyard.
If you care about details of the rules, this is an example of a state-based action. Here's the actual rule:

704.5f If a creature has toughness 0 or less, it's put into its owner's graveyard. ...

State-based actions happen automatically*; others you already know include creatures dying when they've taken lethal damage or you dying when your life is zero. Another state-based action: auras being put into the graveyard when the creature they enchanted dies (like I mentioned with Dead Weight).
One more general thing you should learn here: when an object changes zones, like a creature being moved from the battlefield to the graveyard, it doesn't "remember" anything about where it came from. The creature card in your graveyard doesn't know it used to be a creature on the battlefield, that its toughness was reduced, and so on. It's just in the graveyard, and it stays there. (If you're curious, this is comp rule 400.7. - it does have a few specific exceptions, mostly things that you'd expect are necessary to make cards work.)
* State-based actions don't technically happen immediately; they happen whenever a player would get priority. This distinction doesn't usually matter, though - pretty much, it means the creature dies when the spell or ability finishes resolving, not halfway through, which doesn't usually make a difference.

Also it does not count as "Destroyed"  it just dies without being destroyed.


text:
How would Solidarity of Heroes work with Heroic counter abilities
I have built a Satyr and Centaur ramp deck that works on the heroic ability to boost counters with instant spells. I would like to know how Solidarity of Heroes would effect this ability as it states:

Choose any number of target creatures. Double the amount of +1/+1 counters on each of them.

My gut instinct would be that I control both the heroic ability and the effect that is placed on the stack by Solidarity of Heroes so I could choose which happens first.
So essentially could I target a Setessan Oathsworn with Solidarity, put two +1 counters on Oath with the heroic ability, then double the counters with Solidarity?
My confusion lies with when Setessan is being targeted by the spell to double the counters that puts the heroic ability on the stack, then the spell resolves putting Solidarity on the stack which means it would possibly resolve first doubling zero counters...

Possible duplicate of Does doubling counters trigger Hardened Scales?

@JonTheMon That question appears to be about triggering abilities with the counters being placed so it slightly different... I want to know if when I target Setessan with Solidarity, will I be wasting the spell if Setessan has no counters? or can I activate the Heroic trigger first then double the counters after?

Related, but not duplicate: https://boardgames.stackexchange.com/questions/18175/when-does-heroic-trigger?rq=1

Yes, you can do this, but no, you don't choose the order, so you don't get to choose whether it happens or not.
When you cast Solidarity of Heroes, you chose your targets, and once the spell is cast, anything it targets becomes targeted. This triggers heroic, which goes on the stack on top of Solidarity of Heroes. Heroic resolves, giving you 2 +1/+1 counters, and then Solidarity of Heroes resolves, doubling all counters on that permanent.
Casting a spell:

601.2c Any abilities that trigger when those players, objects, and/or zones become the target of a spell trigger at this point; they'll wait to be put on the stack until the spell has finished being cast.

The Gatherer rulings for Solidarity of Heroes actually address this question specifically (emphasis mine):

Solidarity of Heroes can target any creatures, not just ones with +1/+1 counters on them. Notably, heroic abilities of any target creatures that put +1/+1 counters on that creature will resolve before Solidarity of Heroes.

As Gendolkari noted, you don't get to choose the order in which Solidarity of Heroes and heroic abilities go on the stack.  Heroic abilities aren't triggered until Solidarity has been cast, which includes placing the spell on the stack.  This means that the heroic abilities always resolve before Solidarity of Heroes.


text:
Aligned Hedron Network and Ulamog's Despoiler
If I was to use Aligned Hedron Network against an Eldrazi deck to exile big creatures, am I then able to send these creatures to the graveyard with the likes of Ulamog Despoiler to give him the 4 +1/+1 counters? I'm not sure if the cards exiled this way can be targeted by these types of abilities...
If this works and my Aligned Hedron Network was to be destroyed afterwards, the creatures would not return from Exile as they were placed in the graveyard, Correct?

Ulamog's Despoiler makes no limitations as to what cards can be moved from exile to graveyard except the cards' owners. Therefore, you can move any of your opponent's exiled cards, no matter how they got exiled. Note, however, the rulings on the Despoiler's Gatherer page regarding face-down exiled cards.
If the Aligned Hedron Network was destroyed after Despoiler has had its effect, the Network's effect would end and return all cards exiled with it to the battlefield. Unless a few specific exceptions apply (which they don't here), effects do not track objects across zones, and the Network would not return the cards put into the graveyard by Despoiler.

Ah, that's how I envisioned it working. Brilliant. what I forgot is that Aligned Hedron network would also exile my creatures... and that would cause significant problems unless I destroyed it myself afterwards.

@Nathan: Meh, you have a despoiler, and they have an absence of creatures. You seem ahead to me. What you need is a way to sacrifice the network for value once the despoiler's got his num nums.


text:
Can equipment be re-equipped to another creature?
With Artifact equipment, say I've equipped it to one creature, and I want to move it to another, can it be equipped to another creature if I pay its equip cost again?
My thought process is that they aren't like Enchantment-Aura's which target a creature specifically, more so like an item that is not bound. Am I right in thinking then that they can be equipped more than once?

Yes, if you have an Equipment attached to one creature, you can pay its equip cost to attach it to another creature. Every Equipment has the Equip keyword ability, which is defined in rule 702.6a as

Equip is an activated ability of artifact Equipment cards. “Equip [cost]” means “[Cost]: Attach this Equipment to target creature you control. Activate this ability only any time you could play a sorcery.”

In addition, the Attach keyword action that the Equip ability uses is defined in rule 701.2a as

To attach an Aura, Equipment, or Fortification to an object means to take it from where it currently is and put it onto that object.

So, if an Equipment is already attached to a creature, when you activate its Equip ability, you move it from where it currently is (attached to the original creature) and put it onto the new creature.
One thing to keep in mind is that the Equip ability is an ability the Equipment has, not the creature. So if, for example, a Suppression Bonds is attached to the creature, you can still re-equip an Equipment attached to that creature. However, if the Suppression Bonds were instead attached to the Equipment itself, you would not be able to activate the Equip ability.

The reminder text (present on only some equipment) is a pretty good hint too; it doesn't say anything about the equip ability disappearing after you use it once.

That's a good point. The new Magic Origins game also has a pretty nice explanation of Equipment in the relevant skill quest.

Does this also apply to creatures that have been Locked in a powerless state as with One Thousand Lashes?

One Thousand Lashes prevents the creature from activating abilities. But the Equip ability is on the Equipment, not the creature. So no, it isn't affected. On the other hand, if you attach a Suppression Bonds directly to the Equipment, it would be prevented from re-equipping.

One useful move is to Equip a creature, attack with it, and then in your second main phase, move the equipment onto a creature you plan to block with. Handy, if you've got the spare mana.

Reading though the rules it seems clear to me that if a creature is equipped and then that equipped creature is mind controlled, you can reattach that equipment to a creature you control.
Nobody ever does this though, like ever. The rules seem so clear but I don't want to try this due to fear of being shot down or violating some kind of play etiquette I don't know about.

This isn't really an answer to the question being asked here. If you want to know about mind controlling an equipped creature, you could ask it with the "Ask Question" link: http://boardgames.stackexchange.com/questions/ask

Welcome to the site! This isn't an answer to the question, so it's going to get flagged and/or downvoted. That said, you're correct. The rules are very clear. Gaining control of the creature does not give you control of the artifact equipment. CR 301.5d makes this explicit. (Remember that you can only pay equip costs during the main phase of your turn.) If the people you play with don't play this way, then you need to educate them!

Is there a reason that my flag for this was declined? It seems clear to me that this isn't intended as an answer to the question being asked here, but rather a comment or question about handling equipment on a mind controlled creature.


text:
Can I combo Dismiss Into Dream with Living Inferno or Cauldron of Souls?
So, at the Prerelease this past weekend I pulled a Dismiss Into Dream from the packs I won.
I LOVE the flavor of this card and I think I could abuse it. I wanted to check on rulings though:

Dismiss Into Dream + Living Inferno: Would I be able to declare the targets and then they would all have to be sacrificed before they dealt damage to Living Inferno? And furthermore, could I choose any number and just have them all take 0 damage?

Dismiss Into Dream + Cauldron of Souls: Same sort of question: Could I target them then they have to be sacrificed before the creatures get Persist?

A lot of 7 drops can be "abused" - I think the idea is if you can play a 7 drop in a constructed format, it really should win you the game.

@corsiKa I almost exclusively play casual and limited. And the casual I play is very, very slow multiplayer (most often) which means we get to set up grand strategies and execute them. It's a pretty good time and this card fits perfectly into what I play.

@MiloGertjejansen Here's a gatherer search with more "any number of target creature" options. Sway of Illusion in particular seems to fit perfectly mechanically and thematically. A board wipe when Dismiss into Dream is in play, and draw a card, all for the low cost of two mana! Artful Dodge also seems an exceptional fit.

@ghoppe Thanks! I did see those and I added them to my deck list. I am getting pretty excited for this deck with the release of M14.

Just remember to target one of your own creatures with Sway of illusion so that it still resolves and you get your card! :)

Yes, it is powerful, but for 7 that is to be expected.
Targeting a creature affected by Dismiss Into Dream will have them sacrificed before the spell/ability targeting them resolves. This is because the effect created by Dismiss Into Dream will go on the stack after the spell targeting the creature.
To address your specific questions:
No on your combo with living inferno, a ruling on gatherer prevents you from assigning 0 damage:
http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=96874

You divide the damage among the target creatures as you activate Living Inferno's ability. Each target must be assigned at least 1 damage.

Yes, on your combo with Cauldron of souls.

Oooo this makes me happy. I also am looking at Sea King's Blessing for a U board wipe.. This is extra good since I play multiplayer often, this sort of thing tends to pay off quite well. Thanks for the answer! As a side note, I did read your first paragraph, with the stack. So wouldn't Living Inferno get dealt a ton of damage after all the creatures are sacrificed? Or does his ability look for the creatures at the time of resolution?

@MiloGertjejansen good question... I do not know the answer. The damage dealt to living inferno is determined at resolution time while the creatures are in the graveyard.

Yeah, that's something I would have to look into. Also, it applies for the Cauldron: The cards would be in the graveyard when they gained persist in which case, they probably wouldn't return at all, since they didn't die with persist.

For the cauldron, they would not come back. The wording on persist says something like 'when a card with persist goes to the graveyard and does not have a -1/-1 counter' IIRC. They would be in the graveyard before having persist.

Got it. Cool. Do you know where I could look up something like the ruling on Living Inferno? Or at this point would I have to just find someone who knows the rulings on that?

@MiloGertjejansen Ask it on this site as a new question. There are lots of people on this site that will know the answer.

Done. http://boardgames.stackexchange.com/questions/12482/if-creatures-targeted-by-living-infernos-ability-all-die-what-happens

Living Inferno's ability fizzles.  It never takes damage