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Is time empty of inherent existence?
My understanding of dependent origination is that it asserts that all things are empty of inherent existence. On an intellectual level I can appreciate and accept this however I struggle when it comes to time. Is time included in this? Is it dependent on something else and if so what kind of things are conditions for time? In my mental picture of the world time is kind of a backdrop for everything else but clearly this mental picture conflicts with dependent origination.

Understanding time is an important part of insight into the nature of things. How can you understand the empty nature of entities if you don't understand their relationship with time? How can you be free of self, of the dictate of the form, if you don't see beyond time?
In traditional literature this topic is famously addressed by the founding father of Japanese Zen, Master Dogen, in his essay U-ji - usually translated as "Being-Time" or "Existence-Time". While I would not give justice to it here by quoting or paraphrasing, here are my own limited glimpses of understanding:
Time is not a container. Entities do not "move" through time. Nor the time "moves" while entities "stay in place and age on". Instead, time is existence itself, time is not separate from the state of things. Because entities are empty they do not have an identity that would be retained and would pass from one moment of time to the next. That identity is a conceptual overlay. If you think of transformations like wood=>ashes or milk=>yogurt it becomes very clear. At what point does wood stop being wood and becomes ashes? At what point milk dies and yogurt is born?
...There cannot be such thing as time travel, because the notion of travel itself requires time for the travel to occur in. If you could skip through time, what time would that skipping occur in? Thinking in terms of entities moving through time is a deep-ingrained samsaric thinking.
All compound things exist in some configuration in one point in time, and in a different configuration in another point. Consciousness (awareness) exists as part of that same setup. It looks like it changes, but just like everything else, it just exhibits different configuration at different points in time-space. All phenomena exist as a web of connections across time and space.

"There cannot be such thing as time travel..." Exactly what I thought...

What if time travel is experiencing time faster than what it is now? There are scientific researches which seems to have found that small insects like mosquitoes have a rate of experience of time lesser (slower) than ours.. What if we could mystically alter the working of our brain/whatever to experience time slower or faster than what it is now?

"Faster" requires a clock to measure the speed. 2) In this case experience of time and time travel are two different things. When you experience time "faster" you can't go back, so it's not "travel". 3) This is becoming an idle conversation so I'm inclined to not reply.

Ultimately, Time exists only conceptually, i.e. as a mental formation. Thinking about past, present and future are mental events, happening in the present moment.
We live only for one thought-moment at a time (momentary death).
The mind might be chasing after some object or running away from another object but that also takes place in the present moment, thus we are always in the present moment.
Conventionally, we can speak of Time as existing and exercising some kind of control over beings in conditioned existence. That can be seen in the workings of Kamma. Kamma is fourfold and one of its classifications are called "Time of Ripening"1, i.e. when the kamma is coming into fruition.
There are actions that might produce their effects in this very life, they are called Immediately-Effective-Kamma.
There are actions that might produce their effect in a subsequent life, they are called Subsequently-Effective-Kamma.
Then there are actions that might produce their effects in any life as long as one is in the conditioned realm, they are called Indefinitely-Effective-Kamma.
As seen here Time exists conventionally, as do beings and rebirth, since they are merely concepts, conventions and designations. Ultimately though, these concepts are not findable or inherently existing. In other words they fall under the doctrine of Emptiness (Śūnyatā).
To further illustrate the difference between Conventional and Ultimate reality let's take a look at a quote from the Milindapañhā2 where King Melinda discuss Time with Ven. Nāgasena:

“Nàgasena, when you say, ‘Time immemorial’, what does time mean? Is there any such thing?”
“Time means past, present and future. There are some for whom time exists and some for whom it doesn’t. Where there are beings who will be reborn, for them time exists; where there are beings who will not be reborn, for them time does not exist.”
“Well put, Nàgasena, you are clever in reply.”

As we see here Nāgasena explains that Time exists for beings that will be reborn, i.e. beings that are still wandering in the realm of Samsara.
Time does not exist for beings that will not get reborn, i.e. those who have won Nibbana.

1 Comprehensive Manual of Abhidhamma, Ch. 5: "Compendium of the Process-Freed", p. 201, by Ven. Bhikkhu Bodhi
2 The Debate of King Melinda, Ch. 2: "Rebirth", p. 47, by Ven. Bhikkhu Pesala

Time is merely the concept humans use when trying to apprehend impermanence. Time is the measurement of the rate of change of things around us that are appreciable to the scale of which we experience reality. All conditioned things being unable to maintain a constant form, and thus being in constant flux, give the appearance of "time", but there is no time as we conventionally think of it, only constant change, impermanence. Therefore, time is dependent on greed, anger, and delusion, a misapprehension of reality as it is.

I think this answer implies that (passage of) time depends on (two, separated in time) events.
For example 'the time elapsed between today and tomorrow' depends on 'today' and on 'tomorrow'.
Similarly maybe space (a.k.a. distance) depends on (two, separated in distance) objects.
See also this topic which suggests that there have been conflicting opinions/definitions about whether space is conditioned or unconditioned. An argument for its being called unconditioned is that it's eternal (I'm not sure what the word for "eternal" was, I wonder whether it was akalika i.e. timeless).

+1 so space-time is dependently originated at all. Sounds convenient with Einstein...

Yes, beware that I was taught Einstein's Relativity, so that affects my view: which might differ from a canonical or orthodox Buddhist view.

Funnily Einstein is referred in another answer as well...

The Buddha exclusively used the term 'dependent origination' to refer to twelve conditions that lead to suffering. Once you adhere to the Nagarjuna (Mahayana) view on 'dependent origination' (i.e., cause & effect or conditionality) there will be conflicts since conditionality & the idea of 'no inherent existence' is difficult to apply to all things.
The 'no-inherent-existence' ('emptiness' - 'sunnata') the Buddha was concerned with was the emptiness of 'self', i.e., 'egoism' (SN 35.85). The Buddha was not concerned with the 'no inherent existence' of time since time obviously does not have a 'self', 'ego' or 'personality view'.
Take the laws of nature (dhamma-niyama), which are conditionality, impermanence, unsatisfactoriness, not-self, emptiness, etc. If they lacked inherent existence then they would not exist. How could they be 'lawful'? Even the idea of 'no inherent existence' would have 'no inherent existence'.
The Buddha taught impermanent things naturally cannot be a 'self'. But this does not mean the opposite must apply, namely, permanent things must be a 'self'.
People often ask: "If all things are impermanent, is impermanence itself impermanent?" Naturally, this question is irrelevant since the Buddha only taught conditioned things are impermanent & never taught that impermanence is a conditioned thing. Thus it is reasonable to conclude impermanence is permanent; just as not-self/emptiness (anatta/sunnata) is permanent.

One has to understand that the texts referred to were written in the Iron Age in India. They were not very sophisticated in how they thought about the physical world. For example, they understood it to be made of just 5 elements: earth, water, wind, fire, space. There is no sophisticated discussion of time as a concept. Indeed in the West there is almost no sensible discussion of time until the Enlightenment. Our understanding of time was completely wrong until just a century ago, this year, when Albert Einstein published his General Theory of Relativity.
It's simply unlikely that one will find any satisfactory explanation of time in traditional Buddhist texts.
To complicate things some people (Ñāṇavīra and Buddhadasa) have argued that the Buddha claimed that his dharma was akāliko and that this means that dependent arising cannot be understood in temporal terms. They use the building block approach instead: for example when the walls are present, the roof is able to stay up. When the walls are absent the roof does not stay up (it either cannot be put up or it falls down). The walls must precede the roof in sequence, but the argument is that this does not imply a temporal sequence. I don't find this entirely plausible.
Although the language allows us to talk about time as though it is an entity, this is philosophically untenable. Time is not a feature of the world, it's a feature of how we conceptualise sequences of experiences.
A modern argument would say that time is a Kantian a priori. Like causation, time, is simply a pre-existing concept we superimpose on experience when we observe sequences of events. Hawking argues that the Second Law of Thermodynamics (i.e. entropy increases over time) imposes an direction on time. We can always tell when a film is being played backwards partly because of how we understand causality and partly because of how we understand entropy.
But so what? What soteriological value does this knowledge have? What difference will it make to how you practice or relate to people. None that I can see. The fact is that most of don't need an abstract understanding of time in order to live. If you really want to understand time, then trying to do so in terms of a theory which only seeks to understand how experiences arise in awareness is never going to be very satisfying. There's not a bad description in Stephen Hawking's book A Brief History of Time. Although it is not easy to understand.
I think perhaps that we would need to clarify the purpose of this question. What would one gain by an intellectual understanding of time that is rooted in an Iron Age worldview?

Is it dependent on something else and if so what kind of things are conditions for time?

Time, like any other conditioned phenomena lacks an inherent existence for it also depends on various factors. There's a concept called time dilation from the theory of relativity which shows that time can stretch or shrink depending on the observers and their moving speed relative to each other or the different positions from a gravitational mass or masses.

+1 nice: Modern physics used to explain buddhism...

There is actually concrete scientific evidence that time is empty of inherent existence. This scientific evidence comes from the theory of relativity, together with something about relativity that Einstein himself had not realized. This is the fact that Einstein’s second postulate of relativity — that the speed of light is constant relative to all inertial frames of reference — is not actually a fundamental law of nature but a consequence of the fact that we have defined time in accordance with how we experience the universe.
It is a scientific fact that the rate our body functions is governed by the rate of electromagnetic transmission, since all cells and all organs in our body function via electromagnetism. This means that if we use our conscious experience as the standard for defining our time, we have actually defined time by the rate of electromagnetic transmission, which is the speed of light. That is why the speed of light is always constant — we have actually defined it to be so!
What this means is that we have also defined time according to our conscious experience (which depends on the speed of light). That explains why, in relativity, time distorts depending on the observer's state of motion. Time is thus only an entity that is dependently arisen since it depends on the imputation of the mind that gives it the label “time.” Time does not exist independent of the observer, and hence is empty of inherent existence from its own side. Without the observer, it does not even make sense to talk of time.
A more detailed explanation can be found in my article “Relativity Proves that Time and Space are Empty of Inherent Existence.” http://kenneth-chan.com/physics/relativity-proves-time-space-empty-inherent-existence/. It is probably necessary to look at this longer explanation to fully understand what I am trying to convey. It is just not possible to explain things well in a short answer.
A more mathematical explanation of how time and space are derived from our conscious experience can be found in the paper “Time and Space.” http://kenneth-chan.com/physics/time-and-space/ (This paper was refereed and approved for publication by Professor Kip S Thorne, who is a world authority on General Relativity.)
Please realise that this is concrete scientific proof that the Buddhist Madhyamaka teachings regarding time and space are correct. There are no speculative elements whatsoever in this proof; so even scientists will have to take it into account. Professor Kip S Thorne would not have approved the paper "Time and Space" for publication if the dramatic findings there were based on speculation of any kind.


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Does Buddhism cause longevity?
In this book about Bodhisattvas it says that  traditionally Buddhism can cause longevity in a way that parallels the longevity that is sought after by Taoism. This kind of longevity arises in the same way that the psychic powers do i.e. it is a natural result of practice but it isn't the end point and it isn't something that should be grasped after. This is the first time I have heard of Buddhism in connection with longevity. Has anyone got any further details about this and perhaps some textual references where this is referred to?
Please note - I'm not interested in scientific studies or connections to well-being/stress reduction and similar in this question. I want to focus on the texts and traditions rather than more modern studies.
Many Thanks

Longevity, especially the longevity of the Buddha, comes up quite often. @ChrisW has cited the, probably apocryphal, story from the Mahāparinibbāna Sutta. It's very puzzling and unlikely way for the Buddha to behave, far too arbitrary. If he could live longer, then why not simply do it. Why set up harmless, lovable Ānanda to take the fall. I think this reflects early anxieties following the Buddha's death that things would not continue. However it is, I think, the first reference to the longevity of the Buddha in a Buddhist text.
Longevity is one of the classic payoffs from puñña or merit in the early Buddhist texts, i.e Appamāda Sutta SN 3.17:

Āyuṃ arogiyaṃ vaṇṇaṃ, saggaṃ uccākulīnataṃ;
  Ratiyo patthayantena, uḷārā aparāparā
  appamādaṃ pasaṃsanti, puññakiriyāsu paṇḍitā. (SN i.87)
Life, health, good looks, heaven, a good rebirth
  Every wonderful thing one could wish,
  The wise praise vigilance amongst all the merit making activities.

And the Buddha had acquired an essentially infinite amount of merit. So the question is why did he die at all? This question is actually asked by Ruchiraketu in the (Mahāyāna) Suvarṇaprabhāsottama Sūtra (chapter 2). In response he has a vision which a mandala of buddhas appear and answer his question.

mā tvaṃ kulaputraivaṃ cintaya evaṃ parīttaṃ bhagavataḥ śākyamunerāyuḥpramāṇam / tatkasya hetoḥ / na vayaṃ kulaputra taṃ samanupaśyāmaḥ sadevake loke samārake sabrahmake saśramaṇabrāhmaṇikāyāṃ prajāyāṃ sadevamānuṣāsurāyāṃ yaḥ samarthaḥ syādbhagavataḥ śākyamunestathāgatasyāyuḥpramāṇaparyantamadhigantuṃ yāvadaparāntakoṭibhiḥ sthāpayitvā tathāgatairarhadbhiḥ samyaksambuddhaiḥ / [9-10]
Don't you even think it, good man, that the lifespan of the Bhagavan Śākyamuṇi was limited. What is the reason? Good man, we do not see anyone in this world with it's devas, māras, brahmās, people who are ascetics & Brahmins, with kings, men and lords, who could understand, to the fullest possible extent, the lifespan of Śākyamuṇi Tathāgata, apart from the fully enlightened tathāgatas and arhats.

This is followed up by some verses including

jalārṇaveṣu sarveṣu śakyante bindubhir gaṇayitum /
  na tu śākyamunerāyuḥ śakyaṃ gaṇayituṃ kvacit // Suv_2.1 //
The drops of water contained in all the oceans could be counted;
  But no one can count the life of Śākyamuni

And so on. His apparent life and death are not to be taken seriously. His lifespan is infinite. BTW Sangharakshita covers this material in his talk: The Bodhisattva’s Dream. And also in his book on the Suvarṇa.
Any perceived short-comings on the part of the Buddha become increasingly problematic as time goes on. Apparent faults, such as a relatively short lifespan, are corrected by the invention of new myths and legends as time goes on. The principle reason for a bodhisatva to wish for a long life, is of course the same one that makes them put off awakening, so that they may help many beings.
In Tantra there are specific sādhana practices aimed at bestowing long life. These are often associated with Amitāyus (Whose name means "infinite life"), White Tārā, and Uṣṇiṣavijāya. Some of the relevant ceremonies are described in stephan Beyer's book Magic and Ritual in Tibet: The Cult of Tārā. A brief example is the well known White Tārā Mantra.

oṃ tāre tuttāre ture mama āyuḥ-puṇya-jñāna-puṣṭiṃ kuru svāhā

Although most elements of the mantra are untranslatable the section "mama āyuḥ-puṇya-jñāna-puṣṭiṃ kuru" is a Sanskrit sentence reading "Give me long-life, merit, knowledge and propersity". (BTW The Vulcan salute "life long and prosper might be "āyuḥ puṣṭiṃ bhavatu") One chants this mantra and hopes that White Tārā will bestow these qualities on one. The word "mama" can be substituted with the name of someone else we want to have these blessings.
So we can see that a concern with longevity is actually quite pervasive in Buddhism.

Quoting from Maha-parinibbana Sutta: Last Days of the Buddha,

And the Blessed One said: "Whosoever, Ananda, has developed, practiced, employed, strengthened, maintained, scrutinized, and
  brought to perfection the four constituents of psychic power could, if
  he so desired, remain throughout a world-period or until the end of
  it. [21] The Tathagata, Ananda, has done so. Therefore the Tathagata
  could, if he so desired, remain throughout a world-period or until the
  end of it."
But the Venerable Ananda was unable to grasp the plain suggestion, the significant prompting, given by the Blessed One. As though his
  mind was influenced by Mara, [22] he did not beseech the Blessed One:
  "May the Blessed One remain, O Lord!. May the Happy One remain, O
  Lord, throughout the world-period, for the welfare and happiness of
  the multitude, out of compassion for the world, for the benefit, well
  being, and happiness of gods and men!"
And when for a second and a third time the Blessed One repeated his words, the Venerable Ananda remained silent.
Then the Blessed One said to the Venerable Ananda: "Go now, Ananda, and do as seems fit to you."

So the above is a textual reference.
Off-topic to the question, this (i.e. not having asked the Buddha to remain) is a reason why Ananda was reproached at the first council after the Buddha's death. Later in the same sutta Ananda realizes what the Buddha had been saying and asks him then (asks him three times), but the Buddha says no:

And the Blessed One answered, saying: "Enough, Ananda. Do not entreat the Tathagata, for the time is past, Ananda, for such an entreaty."

and,

"So also at Vesali, Ananda, at different times the Tathagata has spoken to you, saying: 'Pleasant, Ananda, is Vesali; pleasant are the shrines of Udena, Gotamaka, Sattambaka, Bahuputta, Sarandada, and Capala. Whosoever, Ananda, has developed... Therefore the Tathagata could, if he so desired, remain throughout a world-period or until the end of it.'
"But you, Ananda, were unable to grasp the plain suggestion, the significant prompting, given you by the Tathagata, and you did not entreat the Tathagata to remain. For if you had done so, Ananda, twice the Tathagata might have declined, but the third time he would have consented. Therefore, Ananda, the fault is yours; herein you have failed.
"Yet, Ananda, have I not taught from the very beginning that with all that is dear and beloved there must be change, separation, and severance? Of that which is born, come into being, is compounded and subject to decay, how can one say: 'May it not come to dissolution!' There can be no such state of things. And of that, Ananda, which the Tathagata has finished with, that which he has relinquished, given up, abandoned, and rejected — his will to live on — the Tathagata's word has been spoken once for all: 'Before long the Parinibbana of the Tathagata will come about. Three months hence the Tathagata will utterly pass away.' And that the Tathagata should withdraw his words for the sake of living on — this is an impossibility.

Donapaka Sutta:

When a person is constantly mindful,
  And knows when enough food has been taken,
  All their afflictions become more slender
   — They age more gradually, protecting their lives.

this might not be directly towards a book you are referring to, it is just a sutta i can remember regarding longevity on the here and now.

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Can karma operate at the level of groups i.e. collectively?
In the book the Land of No Buddha the author interviews a Tibetan lama in which he talks about collective karma - to quote

All groups have karma that is more than just the collection of the
  karma of the individuals of the group. For example a group can decide
  collectively to start a war.

(pp 76 of above book)
This is the first and only time I have heard of collective karma. Is this a concept purely within Tibetan Buddhism? Is it wider than that or is it perhaps just this lama's understanding and it not really a concept in Buddhism generally? If it is a genuine concept then can someone give some more details and perhaps how it fits in with karma at an individual level?

Ven. Yuttadhammo has made a video called "Ask A Monk: Karma in a Holocaust" which might give you some answers.

Although it is rarely mentioned, group karma also applies to merits. Not just negative karma.

Yes, of course, there can be group karma.
To begin with, individual karma is only a useful approximation. Because of anatta, what we conventionally call individual is merely an assembly point of contributing factors. It is these factors that are referred to as karma. They don't belong to anyone, really.
As per the Hierarchy Theory, useful notions of groups can be arbitrarily designated at any level of observation. Individual being, family, social group, country etc. -- all of these are abstractions. Some of the karmic patterns make better sense when looked from far away, in which case it may be helpful to attribute them to a group.

The concept of collective karma also crops up in the Pāḷi commentarial tradition, though it is not called that.
Karma as we find it in the suttas is hardly unified, but generally speaking it is purely a matter of individual practice. But the theories of karma in the suttas don't seem to have survived in practice - every sect of Buddhism mucked about with the theories of the Pāḷi Canon because they are internally inconsistent.
In my first published article, Suicide as a Response to Suffering, on suicide in the Pāḷi Canon, I noted the example (SN 54.9) of the dozens of monks who committed mass suicide after being taught the meditation on the foulness of the body and the decomposition of the corpse by the Buddha. Now on face value this is a tragic mistake on the Buddha's part, and the tradition seems to have felt that it needed explaining. Buddhaghosa's commentary explains it with a story about the monks concerned being connected by a common fate. They had all lived together as hunters in the past. See Bodhi's Saṃyutta Nikāya translation, The Connected Discourses, p.1951, note 301. In this story the Buddha implausibly knows that the monks are going to commit suicide and can do nothing except relieve their attachment to their bodies, so that suicide is easier. This is all wildly implausible, but presumably Buddhaghosa felt it was better than admitting the Buddha had made a gigantic mistake.
"Collective karma" used to be a favourite subject for arguments amongst Buddhists in the early forms of internet social networking such as Newsgroups and Listservs. I never found such discussions very helpful.
Prof Richard Hayes (aka Dharmacārī Dayāmati) wrote a talk about it for his visiting professorship in Leiden in 2009. Is there such a thing as collective karma? Here he covers the ground pretty well, though he leaves the question of whether the idea has any real value open. Personally I don't see much value in it.

This is probably too long to post as a comment, but isn't totally an answer either, in any case it's something of a reference to this.
This summary is in reference to the commentary of the Dhammapada verses 21-23:
There was some king in the Buddha's time ( I don't remember which), whom had two Queen consorts. One of them was virtuous, the other evil and scheming. The virtuous one had a hand maiden who would buy flowers for her Queen every day, but stole from her in doing so.
The hand maiden would take the money the queen gave her for flowers, keep half the money, and return to the Queen only half as many flowers and she had ought to, the Queen not knowing any better. Until one day, this hand maiden heard the Buddha teach, attained stream entry, and then returned to the Queen, confessing her transgression.
The Queen was not mad, but impressed that the Buddha's teaching was this profound.
Fast forwarding, Ananda ends up coming to the palace to teach the Queen and her attendants, the evil Queen wanting to get rid of the good queen, as the evil queen had qualms with the Buddha due to a past misgiving, but was unable to get at him, plots against the good queen.
The evil queen ends up burning the good queen and her attendants alive in a bed chamber, although while they are burning to death they are able to be mindful and attain the path. It is explained in the sutta that the queen and her attendants suffered this kamma because of a misdeed they all committed in a past life.
They had started a fire in a field where a Pacceka Buddha was in a deep state of meditation. Because of this deep state of meditation, he was unharmed. But they not being aware of this, thinking he was burnt and dead, built another fire around his body to fully dispose of the evidence, and left him. The Pacceka Buddha was fine, but the weight of this action followed them all into this life, all of them suffering the same fate.

It's the story of Samavati, commentary to Dhp vv21-23.

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Why does the Buddha always answer a question if asked three times?
I've read in many places in the Pali canon that the Buddha will answer a question if asked three times even if the Buddha is extremely reluctant to give the answer. For instance in the Talaputa Sutta the Buddha is asked by Talaputa ,the leader of a troupe of actors, about what will happen to actors when they are reborn. The Buddha clearly doesn't want to say (it's not good news) but Talaputa really pushes it and asks him three times

"Enough, headman, put that aside. Don't ask me that."
A second time... A third time Talaputa, the head of an acting troupe,
  said: "Lord, I have heard that [...]  What does the Blessed One have
  to say about that?"

The Buddha gives in and delivers the bad news.
But what is the origin of this questioning technique? Why does he always give an answer if pushed like that? Was it a traditional thing in Indian society at that time or was it just a thing with the Buddha? I've only read this in the Pali canon. Does it crop up in other texts and traditions too?

It might also be the same reason repetition is found throughout the canon, as a mnemonic to aid oral transmission.

It's fairly clear that three times was a social convention for crossing some sort of line; either that or just a convention of the Buddha. See also DN 3:

‘Reverend Gotama, there are four castes: the Khattiyas, the Brahmins, the merchants and the artisans. And of these four castes three — the Khattiyas, the merchants and the artisans — are entirely subservient to the Brahmins. With regard to this, it is not proper that they should not pay homage to the Brahmins.’ This was the third time Ambattha accused the Sakyans of being menials.
Then the Lord thought: ‘This young man goes too far in abusing the Sakyans."

and

Again Ambattha remained silent, and the Lord said: ‘Answer me now, Ambattha, this is not a time for silence. Whoever, Ambattha, does not answer a fundamental question put to him by a Tathāgata by the third asking has his head split into seven pieces.’

Walshe, the translator of the above, gives as a note for the second passage, "A curious threat that (as RD observes) never comes to anything, and is of course pre-Buddhist."
Not sure if the "third time" is also pre-Buddhist, but again, it appears to be some sort of line in the sand for the Buddha at least.

I always assumed it was a skillful means of getting the person to go away as soon as possible. Not relenting after two rebukes, at that point, the Buddha assuming this person was not getting the hint, did what was necessary to return to seclusion.
Although I don't believe I have ever seen any mention of this in the Pali Canon, so this is only conjecture. Conjecture based on the Buddha's teaching of right speech and on the virtue of seclusion.

He avoids idle chatter and abstains from it. He speaks at the right time, in accordance with facts, speaks what is useful, speaks of the Dhamma and the discipline; his speech is like a treasure, uttered at the right moment, accompanied by reason, moderate and full of sense.
  – AN 10:176

In this way, one can see that the Buddha was purposeful in the manner in which he spoke, and as such would not be doing so simply as a cultural norm.

No one knows. It was probably just a social convention of the time.


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Purpose of scattered thing or food under tree?
We often see things scattered under the main tree in the Buddhist Theravada temple yard. There is also fresh fruit cut open. It seems they are put under the tree deliberately and regularly. Does anyone know what is the purpose of this?

What country are we talking about?

The fruit etc is probably offerings to the spirit that lives in the tree. Worship of tree spirits (or dryads) is widespread through South and South-East Asia, and a very common element of traditional Buddhism. In Thailand such spirits are known as Nang Mai.

A Buddhist Tree Shrine, Thailand.
Tree spirits (Pāḷi rukkhadevatā) can be found in the Cūḷadhammasamādāna Sutta (MN 45; p.406 in the Ñānamoḷi and Bodhi translation). Tree spirits along with other nature spirits are also found in the Gilānadassana Sutta (SN 41.10). They are also found in a number of Jātaka tales. According to Bhante Dhammika, in his essay Trees in the Buddhist Scriptures, it was common practice to make offerings to such tree spirits:

Other trees were worshipped and given offerings because the spirits were believed to grant wishes. Milk and water were poured on the roots, garlands were hung in the branches, lamps of scented oil were burned around them and cloth was tied around their trunks (Ja.II,104). There is the occasional mention of animal and even human sacrifices being made to trees. The victim’s blood was poured around the foot of the tree and the entrails were draped over the branches (Ja.I,260; III,160).
Note Ja = Jātaka.

Many animist elements, such as yakṣas and nāgas, are evident at every level of the early Buddhist texts and must have been assimilated very early on.
According to the London Buddhist Vihara website offerings of flowers etc, and food, are made from feelings of devotion and not with the expectation of reward.

In some Asian countries they will set out food as offerings so that hungry ghosts can make merit. In some instances they will even build tiny houses for them.

Feeding local animals is also a form of generosity, it could be for that reason as well. You could wait near the tree in silent meditation until the food scattering person arrives and ask them personally for the best answer.


text:
What is the monastic policy on family visitations?
If one was to ordain, would they ever be able to see their friends and family again? If so, how often? Thank you

If one was to ordain, would they ever be able to see their friends and family again?

The following quote is from the book "The Bhikkhus' Rules
A Guide for Laypeople", Chapter: Intimacy - Touching. The last part of the paragraph is interesting. I have highlighted it:

"If a bhikkhu touches his mother out of affection, then this is still an offence but the lesser one of wrong-doing (dukka.ta). [46] While gratitude to parents was strongly emphasized by the Buddha, the bhikkhu having left the home-life and his family should not cling to worldly relationships. The only true way for him to fulfill his filial obligations is by gaining insight into Dhamma and then teaching his parents."

Here it's stated that if possible one should teach the Dhamma to ones parents, meaning that one will be able to see them again.
There is another quote from the same book, Chapter: Rains Retreat:

A bhikkhu must make a formal determination to be resident at dawn every day in that place for the whole three month period. (There are exceptional circumstances when he may be allowed to be away, but even then he should return within seven days.)[26] These three months are often a special time of study or meditation and so are sometimes known as the Rains Retreat or Rains Residence. This is also the normal time when the young men of South East Asia become monks for the traditional three month period.
[26]: This special leave of absence (sattaaha) can only be taken in order to: visit or nurse ill Dhamma-friends and parents; support fellow bhikkhus who are thinking of disrobing; to attend to some essential duty of the Community; to support faithful lay devotees who make an invitation. (See EV,II,pp.84; 89-90)

Here it's mentioned that a monk is allowed to take leave from the Rain Retreat only under special circumstances, e.g. to visit or nurse ill parents. One should return in seven days.

If so, how often?

I could not find anything within the Theravada Tradition as to how often one is allowed to visit family.
Here is a quote from Plum Village (Zen Buddhism):

When you are ordained as a monk or a nun, you make a commitment to stay with the Plum Village Sangha for the rest of your life.  The Sangha is your family and our monasteries are your home.  Even when difficulties arise, we do our best to live in harmony with our brothers and sisters.
Your immediate family is welcome to visit you and they do not have to contribute to expenses. You can also have leave to visit your family every two years, or, in the case of an emergency, sooner.

There is no problem with it but if gone forth, one would no more participate. The care of the parents is even a task that allows to overstep certain rules and near family a Bhikkhu or Bhikkhuni would be allowed to ask for needed.
Practical, especially in SEAsia, the monasteries are in the towns and villages, not so far from home and usually a going forth does not disconnect them, for a good and for a bad, of course.
Monks and Nun do not forget there family but possibilities to be useful for a good are not bound to blood relation ship.
On the other hand, there are families who have a long tradition, that males would ordain. Sometimes you may find even a whole family ordained or involved in serving in monasteries.


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What "religions" did previous Buddhas practice?
I recently found a book called "A Buddhist Bible".
In it, Buddha refers to that there have been many Buddhas before him.
If Buddha was the one to put the foundations of Buddhism, what "religions" did the previous Buddhas practice?
Does this question even make any sense?

Hi Andrey and welcome to Buddhism SE. We have a Guide and a Resource section for new users that you might like.

According to tradition, as in the Nagara Sutta, Buddhas all discover the path to enlightenment and teach that same path to their followers:

"It is just as if a man, traveling along a wilderness track, were to
  see an ancient path, an ancient road, traveled by people of former
  times. He would follow it. Following it, he would see an ancient city,
  an ancient capital inhabited by people of former times, complete with
  parks, groves, & ponds, walled, delightful. He would go to address the
  king or the king's minister, saying, 'Sire, you should know that while
  traveling along a wilderness track I saw an ancient path... I followed
  it... I saw an ancient city, an ancient capital... complete with
  parks, groves, & ponds, walled, delightful. Sire, rebuild that city!'
  The king or king's minister would rebuild the city, so that at a later
  date the city would become powerful, rich, & well-populated, fully
  grown & prosperous.
"In the same way I saw an ancient path, an ancient road, traveled by
  the Rightly Self-awakened Ones of former times. And what is that
  ancient path, that ancient road, traveled by the Rightly Self-awakened
  Ones of former times? Just this noble eightfold path: right view,
  right aspiration, right speech, right action, right livelihood, right
  effort, right mindfulness, right concentration. That is the ancient
  path, the ancient road, traveled by the Rightly Self-awakened Ones of
  former times. I followed that path. Following it, I came to direct
  knowledge of aging & death, direct knowledge of the origination of
  aging & death, direct knowledge of the cessation of aging & death,
  direct knowledge of the path leading to the cessation of aging &
  death. I followed that path. Following it, I came to direct knowledge
  of birth... becoming... clinging... craving... feeling... contact...
  the six sense media... name-&-form... consciousness, direct knowledge
  of the origination of consciousness, direct knowledge of the cessation
  of consciousness, direct knowledge of the path leading to the
  cessation of consciousness. I followed that path.
"Following it, I came to direct knowledge of fabrications, direct
  knowledge of the origination of fabrications, direct knowledge of the
  cessation of fabrications, direct knowledge of the path leading to the
  cessation of fabrications. Knowing that directly, I have revealed it
  to monks, nuns, male lay followers & female lay followers, so that
  this holy life has become powerful, rich, detailed, well-populated,
  wide-spread, proclaimed among celestial & human beings."

So, all Buddhas essentially practice and preach the same religion.

According to the story which accompanies the Dhammapada Verses 183, 184 and 185,

While residing at the Jetavana monastery, the Buddha uttered Verses
  (183), (184) and (185) of this book, with reference to the question
  raised by Thera Ananda regarding Fundamental Instructions to bhikkhus
  by the preceding Buddhas.
On one occasion, Thera Ananda asked the Buddha whether the Fundamental
  Instructions to bhikkhus given by the preceding Buddhas were the same
  as those of the Buddha himself. To him the Buddha replied that the
  instructions given by all the Buddhas are as given in the following
  verses:
Then the Buddha spoke in verse as follows:

Not to do evil, to cultivate merit, to purify one's mind -
  this is the Teaching of the Buddhas.
The best moral practice is patience and forbearance;
  "Nibbana is Supreme", said the Buddhas. A bhikkhu does not harm
  others; one who harms others is not a bhikkhu.
Not to revile, not to do any harm, to practise restraint
  according to the Fundamental Instructions for the bhikkhus, to be
  moderate in taking food, to dwell in a secluded place, to devote
  oneself to higher concentration - this is the Teaching of the Buddhas.

Each Buddha rediscovers the same path and the same truth all over again, on his own.
You can find this narrated in the Pali Canon for Vipassi Buddha (SN 12.4), Sikhi Buddha (SN 12.5), Vessabhu Buddha (SN 12.6), Kakusandha Buddha (SN 12.7), Konagamana Buddha (SN 12.8), Kassapa Buddha (SN 12.9) and of course, Gotama Buddha (SN 12.10).
Furthermore, the Buddha foretold the coming of the future Buddha, Metteyya Buddha or Maitreya Buddha in DN 26 - to do the same.
Also below:

Then, having known with his own awareness the line of thinking in the
Blessed One's awareness — just as a strong man might extend his flexed
arm or flex his extended arm — Brahma Sahampati disappeared from the
Brahma-world and reappeared in front of the Blessed One. Arranging his
upper robe over one shoulder, he saluted the Blessed One with his
hands before his heart and said to him: "So it is, Blessed One! So it
is, One-Well-Gone! Those who were Arahants, Rightly Self-awakened Ones
in the past — they, too, dwelled in dependence on the very Dhamma
itself, honoring and respecting it. Those who will be Arahants,
Rightly Self-awakened Ones in the future — they, too, will dwell in
dependence on the very Dhamma itself, honoring and respecting it. And
let the Blessed One, who is at present the Arahant, the Rightly
Self-awakened One, dwell in dependence on the very Dhamma itself,
honoring and respecting it."
Garava Sutta (SN 6.2)

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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What is "stream"
The question is really just that - "What is stream"?
I've recently found this forum, and recently started reading some Buddhist scriptures, and I've seen the term a few times and have no understanding of it.

There is also a video by Ven. Yuttadhammo about stream entry: "Monk Radio: Stream Enterer".

Into the Stream --
A Study Guide on the First Stage of Awakening (by
Thanissaro Bhikkhu) says,

The Pali Canon recognizes four levels of Awakening, the first of which is called stream entry. This gains its name from the fact that a person who has attained this level has entered the "stream" flowing inevitably to nibbana. He/she is guaranteed to achieve full awakening within seven lifetimes at most, and in the interim will not be reborn in any of the lower realms.

It includes the following definition,

The term "stream" in "stream entry" refers to the point where all eight factors of the noble eightfold path come together.

"Sariputta, 'The stream, the stream': thus it is said. And what,
    Sariputta, is the stream?"
"This noble eightfold path, lord, is the stream: right view, right
    resolve, right speech, right action, right livelihood, right effort,
    right mindfulness, right concentration."
"Very good, Sariputta! Very good! This noble eightfold path — right
    view, right resolve, right speech, right action, right livelihood,
    right effort, right mindfulness, right concentration — is the stream."
— SN 55.5

The coming-together of these factors is called the stream because it leads inevitably to two things, just as the current of a tributary will lead inevitably to a major river and then to the sea. In the immediate present, the stream leads directly to the arising of the Dhamma eye, the vision that actually constitutes this first awakening. Over time, the stream ensures that — in no more than seven lifetimes — one will be totally unbound.

This definition relates it to The Noble Eightfold Path.


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Should I always put another person's interest before mine?
I try to become a kinder person. Sometimes I feel bad ( guilty) after not doing a service for someone, even if it's not in my benefit to do that thing. How can I understand when it's kindness toward another and when it's "stepping over me"?

Hi Anca and welcome to Buddhism SE. We have a Guide and a Resource section for new users that you might like.

In Buddhism, there are fundamental realizations that help you answer these kinds of questions via direct experience, especially the realization of non-self.
There is in fact no "other" that does stepping on.
There is in fact no "me" that is being stepped on.
You are not just yourself. "You" are the whole universe (in a sense).
Anyway, when you can realize that then you will be able to let go enough to stop feeling sorry for yourself and be able to see things objectively more clearly.
That is what the following advice is based on.
If people did not pay for services and people just gave them away then two things would happen:

Those people would in fact not value the service/gift that they are receiving
The person doing the giving will go hungry and perish, one way or another

Furthermore, this delicate exchange that I am referring to, if disrespected by letting other people "step on you" by not getting something back in value (whether it is the practice itself be it teaching or whatever service you are offering), then they will eventually form a debt with you and a chronicity of theievery in their own mind.
In Buddhist tradition, monks don't just beg and run off after they get a meal. They tend to share dharma with their benefactor.
Something to think about: by letting other people "step on you", you are enabling them to do an evil deed! Do not let them use you! This evil deed is not only their seed of retribution but your own to experience in the future as well.
So be strong, be assertive. Make sure you are happy with the exchange! Give and take value. Even if that value is just the action itself, make sure you are happy with it before doing it and not doing it too much out of guilt or pity. If you have to do it out of pity, then try to assert that you are just "making one exception" so that there is no chronicity in the person's mind (which strangely enough is your mind as well!)
I am sure I lost you somewhere and I would need to talk much longer in order to clarify this deep, deep matter but the following things will help you solidify and strengthen your thinking in this regard as you live in this world.

Read MindOS 2nd edition (the best psychology book that exists)
Read Diamond Sutra Explained
Do Metta meditation
Meditate on the feeling of being "stepped on"... find out where it is coming from... talk to it in a journal. Ask this feeling what will make it feel better and happy. You will have surprising insights when you can open up to.. yourself.

Someone once familiarised me with the word "idiot compassion", and it stuck with me. Even for one on the path of the Bodhisattva, who sees the universe as one being, there's a lot to learn about being wise in compassion.
Buddhist teachings aren't separate from nature, so there's nothing non-Buddhist about learning from one's own body and nature. We can see in our body a beautiful coexistence between disparate organs each with a function, they sometimes cooperate, and other times they can fight each other.
If the stomach was very compassionate and kept an excess amount of alcohol or bacteria inside it without nausea and vomiting, very soon alcohol or bacterial poisoning will kill the entire body. In this case the stomach is carrying out its duty in causing trouble for the body for the sake of greater good.
This isn't violence, this is compassionate coexistence.
A bodhisattva too should take appropriate action to serve the greater good, but how exactly that works comes from experiential knowledge. I don't know of any text or sutra that can teach one suitably to perform so, but a lot of times the right course of action is very clear after a brief meditation.

Answer based in Conventional reality (sammuti-sacca).

It can be quite challenging to deal with people sometimes. Especially when one is practicing the Dhamma and trying to do what's best for oneself and for other beings. This is often a delicate balance that one has to find. It takes practice and often by trial and error, until one becomes familiar with both the Dhamma and the different situations in life. Like any other training, one will improve with time, if one works diligently.
A rule of thumb is to never allow yourself to step on yourself, in order to help another being. You are just as important. Actually in Buddhism, it's greatly emphasized that one gets to know oneself and develop oneself, in order to be able to help other beings. Or else it is like the blind leading the blind.
Helping other beings is an important part of Buddhism but there are many ways to help other people. Sometimes it's just lending an ear or a shoulder, while other times it might be more practical or complex in nature. What is important here is the ethical foundation one is building ones help on.
When performing an action it's important that our intention / volition is wholesome, meaning that it is based in the wholesome roots of "renunciation, good-will and harmlessness". If our actions are based in wholesomeness then the resultants will also become wholesome. That is a feature of kamma, that it produces results corresponding to the ethical quality of the action.
If ones actions are based in the unwholesome roots, i.e. "greed, hatred and delusion", then unwholesome resultants will be produced. An example could be, if another being is asking for ones help but one does not really want to do it or one does not have the time to help, so there arises guilt.
Guilt is an unwholesome mental factor so if one acts upon it, one will experience its results which will be unwholesome. In other words, suffering will be produced.
So how to deal with these things? How to stop creating unwholesome kamma for oneself and other beings?
Buddhism offers a solution called the Noble Eightfold Path which is the path that leads to Nibbana. By following it, one undertakes the training and development of ones mind, meaning that one will gradually reduce the unwholesome roots until they can be eradicated permanently, while cultivating the wholesome roots.
Answer based in Ultimate reality (paramattha-sacca).

As it has already been mentioned, then when dealing with this issue in ultimate reality, there exists no "Self, I or Me". In fact there exists no persons, animals, cars, planets or other conventional stuff. These are merely conventions that when searched for cannot be found.
In order to truly understand this, one will have to do insight meditation. By practicing this type of meditation, one will gain experiental knowledge of reality and thereby realize that there is no person to begin with. When one first begins to see this, gradually ones problems begin to fade away. One realizes that all problems are caused by this non-existing "Self, I or Me", that is identifying with stuff and taking ownership of it.
There is a huge difference in saying: "I am angry" and "Anger has arisen", or "I'm feeling guilty" and "Guilt has arisen". It is the second option one will come to realize by doing insight meditation.
If you would like to read more about insight meditation, references can be found here.
Ven. Yuttadhammo has also made a video series, called "Introduction to Meditation: How To Meditate" and a book called "How To Meditate: A Beginner's Guide to Peace".

1 Conventional Reality & Ultimate Reality

I think this is a standard Buddhist answer but it does not answer "How can I understand when it's kindness toward another and when it's "stepping over me"?"

Should I always put another person's interest before mine?

Firstly, what's the person's interest? It's happiness. No matter what a person does, a person is always searching for happiness, even though at first glance it doesn't always seem like that because we lack wisdom to see it. Nonetheless, due to this very same ignorance, beings don't know how to find happiness.
They could be doing something or wanting something from you, and that same "doing" and/or "wanting", due to their ignorance, will make them even sadder. In such cases, you must not put a person's interest before yours. Instead, you should teach them to act in a different way in order for them to become happier.
Or...
They could be doing something or wanting something from you, and that same "doing" and/or "wanting", will make them happier. In such cases, you must put a person's interest before yours and you should teach them what else they could do to become even happier.
In order for you to know exactly when to put a person's interest before yours, you must first become happy yourself. Thus, you must follow the Dhamma, learn and aquire wisdom. The more wisdom you'll have, the more you'll be happy and the more you'll know how to help others on their path towards happiness.
It's your lack of wisdom that prevents you from knowing when to put another person's interest before yours. What happens when you don't have enough wisdom? You suffer. In your case, you feel guilty when not doing a service for someone. Why? Because you can't discern good from wrong. What is good? Good is doing actions that make beings happier. Wrong is the opposite.
Correct discernment between good and wrong comes from wisdom. Wisdom comes from following and experiencing the teachings in the Dhamma. With wisdom comes liberation from suffering. When you liberate completely from suffering, your wisdom is perfect. When your wisdom is perfect, you'll know exactly what's best for others to liberate from their suffering too. Thus, you'll know exactly when to put another person's interest before yours.

Don't follow blindly ,you have to think and find what is better for common good and do it.
As per kalama sutta " don’t go by reports, by legends, by traditions, by scripture, by logical conjecture, by inference, by analogies, by agreement through pondering views, by probability, or by the thought, ‘This contemplative is our teacher.’ When you know for yourselves that, ‘These qualities are skillful; these qualities are blameless; these qualities are praised by the wise; these qualities, when adopted & carried out, lead to welfare & to happiness’ then you should enter & remain in them.”

"How can I understand when it's kindness toward another and when it's "stepping over me"?"
Like it's been said, there is no "you" to be stepped over.
I would add that it could depend on what is asked of you.
It is kindness if the service genuinely helps the other person in some way or has a positive effect, but if they only call when they need a ride to a party then it is not wholesome to encourage their partying nor is it wholesome for them to party.
If they ask you to teach them to meditate, then it would be very kind of you to do so and it would benefit you as well.

I feel your pain, i don't think it's a good idea to put other's needs in front of your own, please see this article to get out of this thinking:
http://www.whatdoyouthinkmyfriend.com/Treasure/circus.html
Of course sometimes our selfless action can be give hope etc to others, even if we sacrifice our needs for those of a single other person. For example the priest Maximilian Kolbe helped inspire many people by volunteering to take a stranger's place and be killed in Auschwitz
In my experience sometimes people will harass even if i give them what they want, what happens is that the goal posts are moved instead. Unfortunately this indicates that they themselves do not know what they need. My guess is that these people have a big need for caring, empathy, and to have a sense that they matter. Isn't it sad that they are not able to see this, and that they express themselves using punishment or psychological violence? This almost guarantees that they will not get these needs met in their interactions with other people. It would be even more sad if we as Buddhists aren't able to see their beauty
There are many different mental attitudes i've taken over the years (that can sometimes lead to a wide variety of actions long-term). One is - as mentioned above - to focus on their needs. Another to focus on our own needs, we may have a need for care and consideration for example. Yet another alternative that has been useful for me is to work with my thinking, the Sutra "the Parable of the Saw" can help:
http://www.accesstoinsight.org/tipitaka/mn/mn.021x.budd.html
In general i find helping others is one of the best ways to help myself. And vice versa. For example if let my meditation be pleasant i will be pleasant when i'm with other people
Kind Regards,
Tord

To serve

not new
not leaving
not ill
not lacking food
and especially unvirtuose with greedy objectives, people amassing, delight in productivity.

If putting in that neither joy nor good will be attained.
For more and details: [Q&A] Should I always put another person's interest before mine?
Beware to serve identity especially such as group consciousness, e.g. community illusion.


text:
Teachings from Buddhas other than Gautama
I asked this question earlier: What "religions" did previous Buddhas practice?
Now I'm wondering if any teachings from earlier (or later) Buddhas have been passed down to our time. And if not, why?

Yes, the historical Buddha is said to have related teachings of other Buddhas; one that stands out is the Amagandha Sutta, which relates the teaching of Kassapa Buddha. Another is MN 81, which relates some aspects of Kassapa Buddha's life, and some words of Kassapa Buddha:

“The king thought: ‘The Blessed One Kassapa, [51] accomplished and fully enlightened, does not accept from me a residence for the Rains in Benares,’ and he was very disappointed and sad.
“Then he said: ‘Venerable sir, have you a better supporter than I am?’—‘I have, great king. There is a market town called Vebhalinga where a potter named Ghaṭīkāra lives. He is my supporter, my chief supporter. Now you, great king, thought: “The Blessed One Kassapa, accomplished and fully enlightened, does not accept from me a residence for the Rains in Benares,” and you were very disappointed and sad; but the potter Ghaṭīkāra is not and will not be so. The potter Ghaṭīkāra has gone for refuge to the Buddha, the Dhamma, and the Sangha. He abstains from killing living beings, from taking what is not given, from misconduct in sensual pleasures, from false speech, and from wine, liquor, and intoxicants, which are the basis of negligence. He has unwavering confidence in the Buddha, the Dhamma, and the Sangha, and he possesses the virtues loved by noble ones. He is free from doubt about suffering, about the origin of suffering, about the cessation of suffering, and about the way leading to the cessation of suffering. He eats only one meal a day, he observes celibacy, he is virtuous, of good character. He has laid aside gems and gold, he has given up gold and silver. He does not dig the ground for clay with a pick or with his own hands; what has broken off riverbanks or is thrown up by rats, he brings home in a carrier; when he has made a pot he says: “Let anyone who likes set down some selected rice or selected beans or selected lentils, and let him take away whatever he likes. He supports his blind and aged parents. Having destroyed the five lower fetters, he is one who will reappear spontaneously [in the Pure Abodes] and there attain final Nibbāna without ever returning from that world.
(from Middle Length Discourses of the Buddha, Bodhi, trans)

There are probably others I can't think of off-hand, but they all would have to have come from the current Buddha, since the interval between Buddhas is invariably so vast as to not allow for any trace of the previous Buddha's teachings to remain.
(This all from a Theravada Buddhist POV)

In Theravada tradition, a Buddha appears in this world only after the teachings of the previous Buddha completely vanishes. It is also mentioned that the teachings of a Buddha will survive after his parinibbāna only if he teaches the Vinaya pitaka.

There is no evidence external to the Buddhists texts that Gautama ever existed, late references to the Buddha as Viṣṇu in some Purāṇas are part of a move to assimilate the Buddha into Vaiṣṇavism (not before the 8th Century CE). My unpublished article on The Buddha's supposed names, for example, shows that these names were made up some time later for an audience familiar with and probably immersed in Brahmanical culture norms: Siddhārtha Gautama: What's in a Name?
For the lineage of past Buddhas there is no evidence at all, except for some texts composed by Buddhists to support the assertion. The only people who take these texts as anything like history are religious Buddhists. They have precisely the same status as other religious texts which claim to have knowledge beyond the human sphere. We have to take these texts alongside, say, the Genesis chapter in the Bible as myths specific to a time and place. To take them literally is naive at best.
The consensus of scholars is that the stories about the past Buddhas are part of a myth which seeks to make Buddhism seem more authentic to the Iron Age Indian audience by making it seem to be a lineage of teachings. This story exists in tension with the idea that Buddhism is an entirely new teaching. A key article in this line of thinking is Richard Gombrich's 1980 article "The Significance of Former Buddhas in the Theravadin Tradition" (online courtesy of the Oxford Centre for Buddhist Studies).

"[The Buddha] differed from [Brhamins] in his failure to authenticare his position by reference to a long line of teachers. Sages proclaiming bold ideas in the Upaniṣads at least presented their credentials by listing their teachers, their geneaology in sacred lore, all the way back to omse mythical culture hero such as an inpsired reciter of the original Veda. The fabrication of such a genealogy for the Buddha, however, present insuperable problems... [because he had no teachers]."
"The Buddha's authentication could therefore only be mythological. It is here that we find the fundamental raison d'etre for the doctrine of previous Buddhas. A model lay close at hand, in Jainism... that the analogous Buddhist doctrine of previous Buddhas was influenced by Jainism seems much more likely than that the Jains borrowed their doctrine from the Buddhists." (Gombrich p.64)

Another article to read, if you can get hold of it is, Naomi Appleton's  The Multi-life Stories of Gautama Buddha and Vardhamana Mahavira. Buddhist Studies Review. Vol 29, No 1 (2012) [Link is to abstract]
Note also that the lineage lists found in the Bṛhadāranyaka Upaniṣad list many men named Guatama. It was a high status Brahmin name dating back to the Ṛgvedic period (ca 1500-1200 BCE). It's highly likely that the Chan/Zen lineages that link Chan patriarchs back to the Buddha are also fabrications for the same reasons. On this subject see John McRae's book Seeing Through Zen: Encounter, Transformation, and Genealogy in Chinese Chan Buddhism.
Given this, We would not expect such mythic figures to have passed down actual teachings. The teachings we have probably date from a period some centuries after the putative life of the Buddha. However as the other answers to this question show, stories were fabricated and authenticated to make this lineage seem plausible. Gombrich discusses most of these texts in his article.
The Mahāyāna Sukhāvativyūha Sūtras purport to be teaching by or about Amitābha Tathāgata, who lives in another universe than out one, but is able to intersect with our universe at the point of death and guide a being to be reborn in his universe where enlightenment is very easy. A number of other Pure Land sūtras explore similar themes.

Do you have any references to any of this information? It's the first I've heard of these ideas & I'd be curious to know more about it...

I've expanded my answer to include some references. The Gombrich article is probably the key source.

so you think buddha was not visnu? there was this:  https://www.wisdomlib.org/hinduism/book/the-agni-purana/d/doc1083104.html

No Buddhist ever believed that the Buddha was Viṣṇu.  If some Vaiṣṇavas did, more fool them.

The Buddhavamsa (a very late addition to the Pali canon) gives accounts of the 24 previous Buddhas. For each of the past 24 Buddhas, it describes the "three occasions of the Buddha's teaching".
They all started by teaching the same sutta (Dhammacakkappavattana Sutta) this is always the first occasion of a Buddha's teaching.
The second and third occasions of a Buddha's teachings vary according to the Buddha involved. For nine of the 24 previous Buddhas, the second occasion was going to Tāvatiṃsa heaven to teach the Abhidhamma.
Some of the previous Buddhas also taught suttas such as the Mangala Sutta.


text:
Is it possible to be Buddhist by nature, or only by indoctrination?
Lately I've been wondering if I (or someone, any person) is religious, agnostic, etc., by nature.

When you say "by indoctrination versus by nature", are you asking "because they're forced/obliged/required to be versus because they want/volunteer to be", or are you asking "because they're taught to be versus because they discover it for themselves"?

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If I meant "forced/obliged/required" I would say that; "indoctrinate" does not denote any of those words. I try to mean what I say, so taught comes close to le mot juste.

I think so.  I think that a lot of thinkers in the past have independently come upon some of the same teachings of Buddhism, although from what I've seen, they didn't come upon the whole or applied them to sotoriological ends as Buddhism did.  Still, this is suggestive to me.

Many evolutionary psychologists, eg. Justin L Barrett and Ara Norenzayan, do argue that religion is a natural phenomenon. The argument are quite complex. Barrett for example argues that our brain contains various modules or devices. For example the Agent Detection Device helps us distinguish agents that are capable of directed motion, from objects which simply follow the laws of physics.
Having detected an agent another module which Barrett calls Theory of Mind, describes the object in terms of it's desires, motivations, and goals in order to help anticipate how it might act.
However if we mistake a stick for a snake we don't lose much. If mistake a snake for a stick we may die. So better to err on the side of seeing agents. But this means we tend to see agents everywhere. Plus our Theory of Mind Device means that we tent of think of agents as being like us - as having a human-like mind.
Barrett adds another element - the Minimally Counter-intuitive concept. If something we think we see is complete counter-intuitive we won't believe it. If it is completely intuitive, we'll believe it, but hardly even notice that we do. But something that is mostly intuitive but counter-intuitive in small number of ways we not only tend believe it, but to find it interesting and memorable.
In addition many experiences, such as the classic out-of-body experiences, make it very easy for people to believe in mind separate from body. This is more or less the default position for most people. This idea is discussed by Thomas Metzinger, in his 2005 article 'Out-of-Body Experiences as the Origin of the Concept of a "Soul".' Mind & Matter Vol. 3(1), pp. 57–84; I have written a precise for my blog:
All combined we get invisible agents as partially counter-intuitive, but interesting and memorable propositions. For many people these take the form of spirits. Spirits are common throughout the Asian Buddhist world. and some become gods. Of course in Buddhism we have both, but tend to down-play this. Still it's possible to apply these ideas to more abstract concepts like karma as well.
Most of the work of these scholars is focussed on theistic religion. I'm beginning to apply their ideas to Buddhism to see if it can add to our understanding of it. See for example my recent essay on Barrett's work in relation to belief in karma and rebirth: Why Are Karma and Rebirth (Still) Plausible (for Many People)?
Karma is a very important invisible agent that ensures a just world by making sure that people get the rebirth they have earned. Many people of my acquaintance find the twin ideas of karma and rebirth entirely plausible and likely even.
So it seems there is a good argument for saying that most people are religious by nature, but that some are not. It's entirely possible that someone could come to the same conclusions as a Buddhist about the world. Indeed these evolutionary approaches seem to be saying that it is atheism and materialism that require a more detailed explanation. Not believing in the supernatural is almost unknown in traditional societies, and yet it is quite widespread in the West, especially outside of America.

Thanks for the link, esp. to your essay. I'm eager to read it. I think about karma quite a lot for a pseudo-believer.


text:
Can a human being reside both in this world and Nirvana at the same time?
I've heard Samsara as the term to describe a world with suffering. And it's my simple understanding that Nirvana is the absence of suffering. Correct me if I'm mistaken.
My question is fairly simple, i.e., do all beings in this world "get reborn" through karma, or are there ascended beings in this world, living as human beings, free of all suffering?

The Sambhogakāya or enjoyment body is part of the Trikaya.
It is used by enlightened beings to try and help and guide those out of Samsara.
It is only found in the Mahayana and Vajrayana Tibetan traditions. These beings can come and go from our world as they please, and reside in their own pure lands.
Some practices have the stated goal of being reborn in a particular Buddha's or Bodhisattva's pure land, in order to receive teachings directly from them for a lifetime.
There are stories of Bodhisattvas that chose to be reborn in the human realm rather than a pure land, and live entire lives (suffering and all) in our world.
There are also Bodhisattvas that choose to be reborn in the hell realms in order to help beings there.

My question is fairly simple, i.e., do all beings in this world "get reborn" through karma, or are there ascended beings in this world, living as human beings, free of all suffering?

It is correct, that beings get reborned due to their kamma. Kamma means action, but not just any action. The type we are talking about here is volitional action, i.e. actions where intentionality is present. This type of action is kamically potent. Kamma is created by body, speech and mind. It originates from the Mind and is based in either wholesome or unwholesome roots. Volitional actions have consequences, we call that vipakka which means "ripening" or phala (fruits).
The ripening need not to come right away, i.e. in this life. It can also come in the next life or operate across the succession of lifetimes. If you are interested in reading more about kamma and rebirth, references by Ven. Bhikkhu Bodhi, can be found here.
There are beings in this world that are free some suffering, i.e. Arahants and possibly Pacceka Buddhas (silent Buddhas). These Buddhas are self-enlightened and arise between the time of two fully enlightened Buddhas, e.g. our Buddha, Gautama and the next Buddha to be, Maitreya.
If you would like to read more about Arahants, Pacceka Buddhas and Buddhas, Ven. Yuttadhammo has written about all of them in this answer.

The predominant description of Nirvana in the Pali scriptures is experienced in the here-&-now.
For example:

Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life fulfilled, who has done what had to be done, laid down the
burden, attained the goal, destroyed the fetters of being, completely
released through final knowledge. However, his five sense faculties
remain unimpaired, by which he still experiences what is agreeable and
disagreeable and feels pleasure and pain. It is the extinction of
attachment, hate and delusion in him that is called the
Nibbāna-element...
Iti 44

It depends on how you interpret Samsara/Nirvana.  If you give it a psychological interpretation then yes, one can live in Nirvana and be in this world at the same time because suffering is mental and thus Samsara/Nirvana are in our heads, not "out there".
Now if you're talking about what happens after one who enters Nirvana then dies, then that's another matter entirely.  For that, perhaps read up on Nirvana with and without Remainder.

Can a human being reside both in this world and Nirvana at the same time?

Suffering is a way of seeing things. In a sense we are all already in
Nirvana but not seeing it so we are still suffering, so very definitely yes.
LUke 17:21
You won't be able to say, 'Here it is!' or 'It's over there!' For the Kingdom of God is already among you."
We just need to see it. It is so close! That said I have not met someone who could see Nirvanha for any appreciable length of time.

The quote used seems to not be about Buddhism.