text:
Why should we worship statues of Lord Buddha?
Why should we worship Lord Buddha statues with flowers, lights and food, even when we know Lord Buddha is not alive and does not exist? Did Lord Buddha instruct us to do so or is there any other reason?

I am not sure we should worship statues itself as that would be some sort of idolatry. Buddhists worship Buddha, and statue or other image is just symbol, something that bring into our memory good qualities of Buddha. It's mindfulness of Buddha. Statue is a symbol, and symbol is communication which states about its subject, Buddha in our case. Thus, showing respect before statue should be directed to Buddha as Jewel, and not to statue. Mindfulness and respect to the Saint and Teacher is good action.
Btw, Buddha is not disappeared, he stated that he will remain in his Teaching (Dharma).

"Idolatry" is a loaded word, though.

Thanissaro says in many places that the act of respect develops hand-in-hand with learning the path:

In their eyes, the religious attitude of respect is needed for any philosophical understanding to grow. And as far as they're concerned, there's no conflict between the two. In fact, they're mutually reinforcing.
Opening the Door to the Dhamma: Respect in Buddhist Thought & Practice

The veneration of statues with flowers and so on should be a natural expression of your development of the path. The act of putting flowers next to a statue doesn't save anyone or develop anything, but it's an expression of your faith that what the Buddha taught is really worth learning:

Respect is the attitude you develop toward the things that matter in life.

The true Buddha is the Eternal Buddha revealed in the Lotus Sutra. It is not a normal human being. The statue serves as a tool for remembrance, but it's actually an inferior symbol, because it depicts the bodily form of the Buddha. A scroll with written characters is better. A Sutra (text) is more similar to the true Buddha-body than a statue of Siddharta Gautama. The true Buddha-body cannot be expressed or depicted so it expediently reveals itself in ways that are understandable to our feeble minds - such as "infinite buddha" (amitabha) etc. Since the true buddha is formless, it cannot be depicted or potrayed. But since it compassionately discloses itself to ignorant beings, it allows to be depicted in such a way. It's simply a useful device. It's dangerous though, because someone might cling to that body and believe a Buddha's body can decay, break or die. That's not possible according to the Nirvana Sutra - the Buddha's body is permanent & eternal. - To answer your question: what we really worship is the Buddha-nature that is present in every sentient and even insentient being. It's in you & me too.

Aniccä vatha sankhärä,
Uppäda vaya dhamminö,
Uuppajjitvä nirujjhanti,
Te san vüpa samö sukhö.

No one should worship any Statue, in death bed Lord Buddha says not to build any statue of him.
More over He had been saying this all his life that his path is the path of practice not worship.
Now comes your Question why should we worship him ?
Once a king denied to worship a statue, then swami vivekananda asked him to spit on one his fathers portrait, as a result kind was angry.
So we should always keep in mind that the most important thing is to focus our minds, some may need help to keep it focused maybe some statue and some may need breathing techniques, some doesn't need anything, they just sit totally blank, As everything came out of nothing, nothingness is god, having a controlled & focused mind in nothing is all we need to do.

Lets say the Buddha was alive today and you offered Dana to the Buddha. But what if the Buddha does not accept it? Will you still not get the merits for your good intentions and the effort you put into preparing the Dana for the Buddha? It's about the quality of your thoughts throughout the time you spent on it.

Buddha is a Sanskrit word meaning knowledge. Thus a statue of Buddha is a personification of knowledge. Buddhists do not pray to Knowledge (Buddha statue). They venerate knowledge because 'knowledge is power'; they pursuit knowledge.
Theists hope to get power by praying. Teaching of Lord Buddha (Budda is a statue) is for practice, diligent strenous practice, to get knowledge.
See definition of Buddha and Buddhism in Oxford Dictionaries.

There is no reason we have to. There is also no reason I have to. Plus there also is the same reason you don't have to either.
Since you have free will, you can choose to do so however.

No one worshiping Buddha in India, We just ignite candle only .
And so if we gonna experiencing just observe, you'll see Buddha's statue, his face there's lighted spirit, you'll not find with other gods, only Buddha's eyes are closed and peaceful spirit on face.
Peaceful atmosphere you'll feel.
Worshiping means bribe from devotee and want praise through chants; but we don't have to worship Buddha to achieve peace.
He just beyond concept of god and religion.
You can meditate next to Buddha's statue.

Swapnil Correct me if i am wrong,
I think Siddharth was not the first person to become Buddha, though his life story influenced large number of beings, including me.
Buddha does not talked about god ever, because if he would have talked about God, some may believe and some may not.
Kabir, jesus, vivekanand, dayananda, rama, Krishna, meera they all were buddha. but still siddharth never talked about god, So he choose another way of making us understand.

Buddha was only first person from where start Buddhism. Buddha wasn't anyone of them you mentioned above; rama, krishna and hinduism story and myth generated by brhamins to corrupt Buddhism knowledge; they tried harm Dhamma. Buddha isn't incarnation or being into them as you mentioned. Read Buddha and his Dhamma from Dr. B. R. Ambedkar rather than myth about Sidharth Gautama spread by brhamins. Buddha's future was told by Asit Muni. Remembre Buddha never taught violence as you mentioned rama, krishna not even vishnu.

The Buddha never asked to be worshiped, he only asked that we use the Dhamma and Vinaya as a guide to cessation. Respect and veneration of the Buddha are wonderful, in that they engender a respect for their Buddha,  Dhamma and Sangha, but valuing the Buddha as anything more than a teacher will likely lead to attachment and stress/suffering.
The Buddha shined a lamp onto an individual path, one without an idol - where the cessation of stress/suffering is realisable in the here and now, generally with him as a guide.
In the Kalama Sutta he denies the absolute validity of all speculation, no matter what this speculation is grounded in, rather asking each one of us to search out and find out the knowledge found in the Dhamma for ourselves!

Good householder,
It depends on where one could find a useful perception of what is worthy for Veneration (pi apacāyana, apa + cāy root pūja = abound, scarify; verb apaciti; gārava, one of the meritious deeds, for a disciple, actually a matter of Sila, conduct . People, and training, usually starts outwardly, by body and speech. If starting unwardly, but not used outwardly, it's difficult when dependend on community, and leads to confusion and conflicts.
Western, modern, have really a hard in doing basics, doing giving and obligations, and certain rationalisation are wonderfuul tools for defilement so that pride and greed would win.
It's usuall in the good following Sanghas and Parisas to venerate the first Gem by body and speech as well and there is also a tradition chant, vandami (veneration), incl. "I will bow down to every Buddha-image".
On the other had, of course, the Buddha actually never allowed to make a Buddha-image to be reminded on the training, saying that people would be to much attached to form/body. He adviced to either use his rests, Chediya (to be reminded on impermanence), or the Bodhi-tree (to be reminded on his awakening).
See Q&A Buddha-images are allowed by the Buddha (at least by monks)?
On the other side, don't one forget that paying proper respect is a grave duty not only in the community but also toward ones teacher.
Here again also the reminder in the Dhp-story, wher all monks gathered to venerate the Master except one, who was the critisiced for not coming by the monks. The Buddha told that he wasn't guilty, since he prefered to eager practiced and payed so highest homage. Yet, think, what are you doing instead of veneration?
How ever, again, it's good to follow the measures of Sila of a community first, and the bow down, paying respect symbolical to the Buddha, is usual observed conduct in the Buddhas Sangha and Parisas. Not doing such will cut you off from the community, as suspected disrespectfull of which, if so, is also a grave, dispelling, transgression, actually (or at least seen as not of much faith and effort in basic trainings).
Remember the ascetic who practiced veneration all his life eager. Good prepared in needed devotion, on hearing just view words of Dhamma, he quickly gained Arahatship.
All you here, coming from total unskillful areas of daily conduct, not used to be grateful and respectfull all day long, not used to fall for more sublime, full of conceit and self-overestimation, would do good to take on what ever as "naive" perceived simple practice, if really wishing to progress instead of nourish defilement, and the matter of grave aversion should actually already be a sign that there would be the way to win over oneself.
See Veneration: Paying respect to teachers, monks - western/modern shamelessness
Only short time ago, devoted asked of what is right and better, to bow down the Buddha-image first, or the Sangha, the actual teacher. They where told that where ever they see more use in it (a Buddha image wouldn't teach, or give you anything in action), where ever you could perceive the Tathagata/Dhamma better, best, there it is good to start this good practice.
Respect, veneration, confidence and patient, are the basics, and especially, as many of you don't really progress, the base forms the path, and Saddhā (faith, from saddha=> sacrifice, falling (of the five kandhas at least), is the cause of the lokuttara paṭiccasamuppāda, the path.
Good generously given further read Respect, Confidence and Patient
Practice it, no problem to gain much understanding and insight, doing simply Vipassana in this way (look Bhante Yuttodhammos teachings on it: Chapter Five: Mindful Prostration, from "How to meditate-A Beginner's Guide To Peace", although he actually had mistreaded a lot of you here with his pseude-liberal approaches for inmature), for for now most of you here can neither except to be perceived as part of the Parisa in your conducts, nor do most actually have a valide/good refuge in the Gems and resisting outwardly of the Sāsana, doing a lot of harm for many and yours.
If you are not able of outwardly sacrifices and proper conducts, how do you seriously ecpect being honestly able to do such on much, much more refined level? Throw away you useless excuses as soon as seeing their cheating for the sake of Mara.
Incapable for Sila, incapable for Dana, no refuge... how do you expect to ever get right concentration, even Jhana, fruits or paths, caught in all kinds of macchariya, formost vaṇṇa-maccariya here.

Vandāmi bhante cetiyaṃ, sabbaṃ sabbattha ṭhāne, supatiṭṭhitaṃ sārīraṅka-dhātuṃ, mahā-bodhiṃ buddha-rūpaṃ, sakkāratthaṃ.

I revere every stupa established in every place, every Relic of the Buddha's body, every Great Bodhi tree, every Buddha image that is an object of veneration. (derived from a talk to Ananda in J479

[Note that this isn't given for stacks, exchange, what ever world-binding trade, but for release from this wheel]


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Are there any differences in karma?
Is there a difference in karma of giving someone $ 1 and giving someone $ 1000, or its same for anything given?
and
Is there a difference in karma of killing a small animal (like mosquito or small fish) and killing an big animal (like a cow or an elephant), or the karma is same for all killings ?
If there is a difference what makes the difference?

I know the answer for question 1.
Given the receiving party and donating party is identical in both cases, giving $ 1000 is worth than $ 1. Hope someone will come with the exact source to support this.

The difference will always be the mental state of the person performing the action. Giving is dependent on one's state of mind while giving; the amount is intrinsically inconsequential (though obviously a poor person will feel more strongly about giving $1000 than giving $1). As Sakka, king of the devas of Tavatimsa says in the Vimanavatthu:

"Natthi citte pasannamhi, appikā nāma dakkhiṇā;
Tathāgate vā sambuddhe, atha vā tassa sāvake"ti. (vi. va. 804);
There is not, when the mind is confident, such a thing as a small gift,
In regards to a Tathagata, fully enlightened Buddha or, furthermore, his disciples.

Giving to the Buddha is considered to be of greater merit, not because of the benefit to the Buddha, but because of the ability to inspire faith and confidence in the giver.
As for killing, the mental state involved in killing large animals is generally more intense; also the sense of the weight of the act is greater, so the mind will be more strongly affected by it. Killing virtuous people, parents, etc. is even worse, because it sets one squarely against virtue.
But there is no hard and fast rule here either; if you obsess over killing a single mosquito buzzing over you at night, you may cultivate more unwholesomeness than a single act of killing a larger animal.
Furthermore, karma isn't a single act of killing; it may be cultivated every moment; every thought concerning a moral or immoral act is karmically potent, so it's imprecise to ask if x or y is good or bad, better or worse, since karma is only a single thought moment at a time, and thus the potency depends upon the nature of the individual mind states.

Yes, there is a difference, and it is in the intent of the action. If you kill a frog out of cruelty, that's a much worse karma than when you kill a snake to protect someone.

Yes, there are.
It is not same as giving someone $1 and giving someone $1000. Similarly it is not same as killing a small animal and killing a big animal. Of course the action is the same, but the resulting emotion or the experience created in the object that is acted upon is not same. Hence, the magnitude of karma varies.
If you give a man $1 he may not feel that happy or grateful to you, but if you give him $1000 then he will feel more grateful and happy. He will feel indebted to you and this will create a stronger karmic link. For real life scenario just think which person will like to help you more, the one you gave $1 or the one you gave $1000? What makes the difference? The experience of the emotion created in their mind through your action. Hence, if you give a person $1 who is starving without food will create more positive karma than if you give $1000 to a rich person like a millionaire.
Similarly, when you kill small animals like a mosquito the resulting effect is less because the suffering they feel is less. The developed the consciousness and self identification of an animal is, the more suffering it is likely to feel at its death. For example, a mosquito will hardly think of its family and children while dying compared to a mammal animal like an elephant or a human.  Since apart from physical pain mental suffering and experience of the object also matters, the more the animal feels the combined pain, the greater the karma involved will be.

Even the earthly law (as in courts) doesn't operate this literally. And the Karmic law is a whole lot wiser. It's a mistake to think of the Karmic law as a tit for tat. The intention as well as the state of the doer matters. The same action may have a different Karmic consequence based on the state of the doers.
Giving $1 to someone may be a very hard thing for a poor man to do while Giving $1,000 to someone may be a very easy thing for a rich man to do. Additionally, one may be giving with the intention of sating their ego - to feel good about oneself - while the other may be doing it due to genuine goodwill.
Many more such factors would be taken into account by the Karmic law. So, yes, there is a difference.

Karma is determined by:

intensity of ones own volition, and
mental state of the recipient (which acts like an amplifier)

Killing a insect may not be as harmful as killing a person as the insert has a lower mental state.
If you give to a pious person and non pious person then the Karma from giving to the pious person is more.
If you give a small sum with a strong volition it will give better results than giving a large sum with a weak volition.

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What is the role of karma in rebirth?
Rebirth is not reincarnation.  How then does the karma of an individual affect their rebirth?
In reincarnation, an individual's karma results in a better or worse next life for their soul. But in rebirth, there is no soul. So why should we care about our karma regarding our rebirth?

I'm not sure I understand how these two sentences are related. Can you elaborate?

In reincarnation, an individual's karma results in a better or worse next life for their soul.  But in rebirth, there is no soul.  So why should we care about our karma regarding our rebirth?

Can you update your question so people will be better equipped to answer?

Thanks for the update :) Why should we care about karma at all? We change from one moment to the next, so really we're born every moment, yet it obviously changes us from moment to moment.

@Yuttadhammo I agree but I'm still pondering anatta, karma and rebirth. :-)

In reincarnation, an individual's karma results in a better or worse
  next life for their soul. But in rebirth, there is no soul. So why
  should we care about our karma regarding our rebirth?

There is no Soul, but still there is consciousness. All suffering we are experiencing now  (in this life) is caused by past unwholesome deeds. So why cause suffering for future life? Yes, that person will not know about us, but still his consciousness will be in our stream of consciousness, related to ours, and even though we will not know why, we will suffer (or enjoy fruits of wholesome deeds).
Different argument. Basically, consciousness in our current life is as changing as between the lives. So, from this point of view, there is no difference when to suffer (or enjoy) - in the future of this or next life. If you don't want to suffer in this life why would you cause suffering in the next?

But in rebirth, there is no soul

The Buddha didn't say there was no soul.
The problem with saying there is a self or there is "no self" requires a view which the Buddha said was incompatible with the practice:

... a certain monk said to the Blessed One: "Which birth, lord? And whose is this birth?"
"Not a valid question," the Blessed One said.
  If one were to ask, 'Which birth? And whose is this birth?'
  and if one were to ask,
  'Is birth one thing, and is this the birth of someone/something else?'
  both of them would have the same meaning,
  even though their words would differ.
  When there is the view that the soul is the same as the body, there isn't the leading of the holy life.
And when there is the view that the soul is one thing and the body another, there isn't the leading of the holy life.
  Avoiding these two extremes, the Tathagata points out the Dhamma in between: From becoming as a requisite condition comes birth."
SN 12.35

He didn't say the one thing (there is a self) or the other thing (there is no self), he said the thing in the middle, which is that with certain phenomena as a requisite condition, other phenomena arise.
He didn't answer the big question of what does and does not exist, he answered the small question about how a thing arises.
Some reading: No-self or Not-self?

So why should we care about our karma regarding our rebirth

One thing that the Buddha consistently affirmed, though, is the efficacy of action and the results of kamma. He would go out of his way (MN 101) to refute ideas that personal action had no consequences or was totally predetermined.
He just didn't link together action and an individual's identity through multiple lifetimes or say that they weren't linked. Either view prevents the living of the holy life.
Seeing action as efficacious and producing results is the thing that is necessary; understanding the arising of phenomena is necessary. Talking about souls is not necessary.

As I've said elsewhere (here and here), death is just a concept. The reality is that the mental and physical aspects of experience arise and cease incessantly, and are governed by complex laws of cause and effect (i.e. karma). Since this process isn't categorically affected by conceptual death, you should be as concerned about how your karma will affect your next life as you are about how it affects this life (or unconcerned, as the case may be).
There is one proviso to that, of course; death is a profound experience that resets much of the nature of one's experience, leaving one without much familiar to cling to; it is thus a time of vulnerability, where one is more prone to cling to past karma and be reborn according often to a seemingly random mind state that just happened to pop into your head at the moment of death. Dangerous for those without mental clarity.

I'm confused. Your statement appears to imply that there is such a thing as a soul.

It's the same reason why you eat good food instead of spoilt food. Because spoilt food gives you a stomach ache. It's a simple matter of causes and effect. There's no soul involved at any place.

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What is it that is re-incarnated ?
I have been reading Mahayana philosophy.
It proposes non-self and that self does not exist in the 5 aggregates.
If the self/atman does not exist, what is that is re-incarnated?
How can nothing reincarnate ?

I would argue it's kind of a soul, but that answer is not well accepted in Buddhist philosophy. http://buddhism.stackexchange.com/questions/26/if-there-is-no-soul-how-can-there-be-rebirth/50#50

Yes coming from a Hindu background, Atman sounds logical to me but since Buddhism proposes Anatman, I want to know how re-incarnation is logically tackled.

I doubt there is any convincing answer regarding this in Buddhism. Due to a certain amount of bias Buddhist followers wont accept the existence of soul, but that leaves the question of identity open as I had raised in that answer.

I disagree with marking as duplicate. The answers to the other question don't explain what is reincarnated, while the answers to this one do.

Forget death! Nothing goes from this moment to the next, even when you are alive. Hold one end of a spoon with your left hand and tap at the other end with your right.Your left hand will feel the vibrations as you tap. Now, do you think you felt it because the atoms at the right side of the spoon travelled to the left? Or is it because the particles at where you tapped vibrated 1st and caused the adjacent particles to vibrate as a result and that caused the next set of particles to vibrate and so on? Likewise, life/death/rebirth are just causes and effects. Nothing goes from preset to the future.
.

I like the wave comparison!

There is neither not self nor self.
The five aggregates; form, sensation, perception, mind formations and consciousness; disperse at death.
Consciousness is life-force. By itself it is without physical form, all types of mental habits, thoughts, ideas, prejudices, compulsions, decisions, familiarity and judgement as to whether an object is pleasant, unpleasant or neutral.
The stream of consciousness passes from one life to another; during this process it is not entirely the same nor entirely different. With the cessation of consciousness samsara ceases.

Stream of consciousness? But most people don't remember previous lives...

Stream of consciousness and name-and-form support each other. When a consciousness has a different name-and-form it is different (not completely different not completely the same). Stream of consciousness is more like life force than memory. Think of it like the flame of one candle being used to light the flame of another candle.

Instead of relations of beings by constant atman, as in some other religions, in Buddhism the relation is causal. So, new being's birth is causally related with past lives. What is carried on to new life is merit and demerit of past actions.
Additionally, in Mahayana's philosophy of Yogacara there is additional consciousness, called alaya-vijnana, which support transmigration.

I like this term "causally related with past lives". Sounds convincing since it is within the framework of dependent origination.


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Buddhist teachings on nation building & politics
From what I have read, Buddhism seems provide a practical path to follow in everyday life for a commoner to lead a life with lesser Dukkha and a rigorous path aimed at Monks seeking nirvana.
But do any Buddhist teachings prescribe rules for nation building and politics?
For example, in Hinduism (Sanathana Dharma), there is Arthashastra which gives a Dharmic way to engage in politics and run the country.
Since there are nations whose state religion is Buddhism (Cambodia, Bhutan, etc), does Buddhist teaching have anything about laws for governance (like the Sharia law in Islam)?

The clearest example of this that I can think of is in the Mahaparinibbana Sutta (DN 16) where the Buddha was asked (obliquely) by the brahman Vassakara on behalf of King Ajatasattu whether he had a chance at killing off an enemy nation. The Buddha replied with the seven "Conditions of a Nation's Welfare":

At that time the Venerable Ananda was standing behind the Blessed One, fanning him, and the Blessed One addressed the Venerable Ananda thus: "What have you heard, Ananda: do the Vajjis have frequent gatherings, and are their meetings well attended?"
"I have heard, Lord, that this is so."
"So long, Ananda, as this is the case, the growth of the Vajjis is to be expected, not their decline.
"What have you heard, Ananda: do the Vajjis assemble and disperse peacefully and attend to their affairs in concord?"
"I have heard, Lord, that they do."
"So long, Ananda, as this is the case, the growth of the Vajjis is to be expected, not their decline.
"What have you heard, Ananda: do the Vajjis neither enact new decrees nor abolish existing ones, but proceed in accordance with their ancient constitutions?"
"I have heard, Lord, that they do."
"So long, Ananda, as this is the case, the growth of the Vajjis is to
be expected, not their decline.
"What have you heard, Ananda: do the Vajjis show respect, honor,
esteem, and veneration towards their elders and think it worthwhile to
listen to them?"
"I have heard, Lord, that they do."
"So long, Ananda, as this is the case, the growth of the Vajjis is to
be expected, not their decline.
"What have you heard, Ananda: do the Vajjis refrain from abducting
women and maidens of good families and from detaining them?"
"I have heard, Lord, that they refrain from doing so."
"So long, Ananda, as this is the case, the growth of the Vajjis is to
be expected, not their decline.
"What have you heard, Ananda: do the Vajjis show respect, honor,
esteem, and veneration towards their shrines, both those within the
city and those outside it, and do not deprive them of the due
offerings as given and made to them formerly?"
"I have heard, Lord, that they do venerate their shrines, and that
they do not deprive them of their offerings."
"So long, Ananda, as this is the case, the growth of the Vajjis is to
be expected, not their decline.
"What have you heard, Ananda: do the Vajjis duly protect and guard the
arahats, so that those who have not come to the realm yet might do so,
and those who have already come might live there in peace?"
"I have heard, Lord, that they do."
"So long, Ananda, as this is the case, the growth of the Vajjis is to
be expected, not their decline."

http://www.accesstoinsight.org/tipitaka/dn/dn.16.1-6.vaji.html
Besides being one of the few examples of the Buddha offering advice on how to run a nation (he was the one who taught the Vajjis these conditions), it also shows how the Buddha never did take sides in political struggle; rather than chastising Ajatasattu, he just taught the dhamma as he always did.

Thanks. This clarifies what Buddha Himself said. Is there anything else which the successive Bodhisattvas(after the Sakhyamuni) said about nation building & war rules?

I don't follow their teachings, so couldn't tell you, sorry. Might want to check out the King of Thailand... he's said a lot of things like "Our duty is not make all people good; our duty is to prevent bad people from getting positions of power."

Nation building is achieve through giving capital, supporting agriculture, protecting the business and farming community, increasing and strengthening the military, being a virtuous and exemplary government and a leader, etc.
This is mainly covered in the Cakkavattisihanada Sutta as well as Mahaparinibbana Sutta (as in the above answer).

A king who follows the ways of Buddhism, by role, perfectly, is called a Sakvithi King. He generally rules by consulting wise men on all of his decisions. Such a king, himself, is a very righteous person in a Buddhist context.
Such a king, is known to come to automatically possess a Sakvithi Gem which appears at his possession due to his worthiness (by character) to rule as a Sakvithi king.


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Syllables and Prayers During Guru Yoga
A while back I was at a workshop by a Yungdrung Bön abbot who taught Guru Yoga using a visualization of the Master with a crystalline body where you visualize being purified first by fire, then wind, then water followed by beams of light radiating from the Master's brow-to-your-brow, throat-to-your-throat, and heart-to-your-heart.  When this happens and at several other points there are specific prayers and syllables that are prescribed.
I found a similar version in Healing With Form, Energy, and Light by Tenzin Wangyal Rinpoche which gives the ritual there, but without the strictly Tibetan elements. It clearly has the same bones (which is not surprising), but it doesn't contain the prayers or syllables.
My question is: Does someone know the full version with the syllables and words intact (in any version, recognizing that there may be several variations) and/or a lead on where I might find it?

Buddhism and yoga have two difference perspectives, This question isn’t related to Buddhism.

It comes straight out of the Yungdrung Bön tradition–among potentially others–and is part of the preliminary practices. Thus, it is very, very Buddhist. See also this link: http://www.rigpawiki.org/index.php?title=Guru_Yoga

Maybe it has some influence from the Mahayana but not with the Theravada

It is found in Vajrayana and Bön. I am not sure that the various forms of it are the same or I would expand the tags, but I have at least two sources on it in this form in the Bön tradition.

Just the prayer and syllables in question, not the surrounding prayers and other elements of the practice (e.g., the refuge prayer), but this is the prayer that I was thinking of (བླ་མའི་རྣལ་འབྱོར, called the "lamai naljor prayer", also transliterated as "lamé naljor", or translated as "Guru Yoga prayer"):

སྤྱི་གཙུག་བདེ་བ་ཆེན་པོའི་ཕོ་བྲང་དུ།
  དྲིན་ཆེན་རྩ་བའི་བླ་མ་ལ་གསོལ་བ་འདེབས།
  སངས་རྒྱས་སེམས་སུ་སྟོན་པ་རིན་པོ་ཆེ།
  རང་ངོ་རང་གིས་ཤེས་པར་བྱིན་གྱིས་རློབས།

Transliterated:

Chi tsuk dé wa chen pö po drang du
  Drin chen tsa wé la ma la söl wa dep
  Sang gyé sem su tön pa rin po ché
  Rang ngo rang gi shé par jin gyi lop

It has been translated as:

On the crown of my head, in a palace of great bliss
  Benevolent root lama, I pray to you.
  Precious one that reveals that my own mind is Buddha,
  Bless me to recognize my own true nature.

I have also seen it translated a little more poetically:

From the crown of my head, palace of great bliss,
  I pray to you, benevolent root lama.
  O precious one, grant me the blessings
  To recognize my own true nature as a Buddha.

There is a version of this practice found in Opening the Door to Bön by Latri Khenpo Geshe Nyima Dakpa Rinpoche, in the 5th preliminary practice, "Connecting With the Teacher", which provides a virtually identical prayer with a slightly different transliteration and another translation.
It also includes a lot of the surrounding details, visualizations, and prayers. This version of the practice is subtly different from the one that I learned, but the bones are very similar if not identical.
The three syllables are:

AH – White, Forehead
OM – Red, Throat
HUNG – Dark Blue, Mind

These are Bön-specific seed syllables and other branches sometimes use variations.
I don't own the book and so can't speak to its contents in any great detail, but Dilgo Khyentse Rinpoche has written a book called Guru Yoga: According To The Preliminary Practice Of Longchen Nyingtik would seem to cover the practice from a different angle.

The prayer you cite is the 4th part of preliminary practices, so called Ngondro. Before doing them, one has to complete refuge (prostrations), purification and Mandala practice. Also, one normally receives lung from the teacher which is oral permission to practise this. If you want to practise Guru Yoga on your own, be sure there is permission to do so. Online you can find 16th Karmapa meditation text which can be done without preparation.

Since you seem very adamant on this point, I'll make it clear that I have received verbal authorization to practice it.

So why do you publish it publicly to others who did not receive the authorization?

Two reasons. 1) Different traditions view the secrecy and restrictions around it differently. Tenzin Wangyal Rinpoche published a version for public consumption in 2002. Nyima Dakpa Rinpoche published a version for public consumption in 2005. It is available on the website of a retreat center and the prayer was published on their Facebook page. The knowledge is out there and not oathbound. 2) Just like with answers to martial arts questions, there is a difference between "can I learn this from a book?" and "I would like a reference to go back to." The latter is something that SE sites do well.

I'd suggest that continuation of this discussion go onto the meta since it will have site-wide implications in how questions get answered.

I am a Vajrayana practitioner and Guru Yoga is our core practice. It has nothing to do with 'yoga'. It translates as ‘Meditation on the Lama’ (Skt. Guru Yoga, Tib. Lami Naljor) and its goal is to realize the nature of mind through identifying with the Lama.
It is a profound practice and I am not sure whether it is appropriate to share the details publicly. Normally one should receive explanations in person from a teacher or some experienced practitioner. I can imagine there are many variants of Guru Yoga as there are plenty of lineages and people have connections to various Lamas. The most important is to trust the Lama that he indeed represents perfect qualities which we want to identify with.
If you want to practise this meditation, the best would be to find a Buddhist centre from Vajrayana tradition and try to receive the explanations there. Please note that some forms of Guru Yoga can only be practised after completing Ngöndro (preliminary practices) which can take a couple of years.


text:
Relationship between Buddhism, Hinduism and Yoga?
All these 3 philosophy/religions are born across Tibet/Nepal/India and they all share numerous concept and practice.
Some points of connections could be:

Noble Eightfold Path are very similar to Yamas in Yoga
Concept of Reincarnation
Karma
Meditation approach as technique to reach enlightenment
Meditation positions: actually the lotus posture, usually used in Buddish for meditation, is a yoga asana
Yantra
Mudras

More in general:

Hinduism and Yoga are almost on the same line, they born in the same time and are based on same concepts.
Buddhism, instead is more "modern", Buddha is dated between 563 BCE to 483, Hinduism/Yoga are thousand of years older, and in someway it is a consequence of the first two:
it is born in an environment where Hinduism/Yoga concept were the basement of the culture.

One of the main difference is:

Buddhism doesn't speak about God but speak about "life and how to live" or better how to stop to suffer. ( so it is basically the oldest psychoanalytic method known )

Personally I believe that the reason behind this (non speaking about God) is because Buddha is like saying "Before speaking about God, you need to be ready and stable and find your self" or better "you don't need to speak about God, you have to find it and the shorter and safer path is inside you."
Main Point of the question:
Define a relationship between the above entities as they are strictly related and so point out the elements of difference that Buddhism philosophy introduces.
I think that this can be helpful to anyone that is approaching to Buddhism.

I have also posted a similar ( but different ) question on meta: http://meta.buddhism.stackexchange.com/questions/22/should-we-consider-also-yoga-philosophy-here

Hinduism & Yoga aren't 2 different things. They are the same.
Yoga is one of the 6 main Darshanas of Hinduism. I.e it provides it's own path for liberation. Other Darshanas(Advaita, etc) too use Yoga as a valid means but not the only valid means.
Can't really say Buddhism is modern. It evolved along with Yoga both of which can be traced to around 4th century BCE.
Both Hindu Darshanas & Buddhism evolved influencing each other. For example Advaita borrowed some of it's elements from Nagarjuna. Tibetan Buddhism incorporated Tantra which is considered 'Hindu'.
Tibetan Buddhism has it's own version of Yoga called Trul khor.
Hence to answer your question, they all belong to the same family, the Dharmic family and have influenced each other.

what I meant for "modern" is that yoga is supposed to start 3-4 thousand years BCE ...

... which is total nonsense. Not even the Vedas are that old.

Old is a relative term. Vedas are said to have been completed into cannons around 1000 BCE.Buddha lived around 500 BCE. If that is not old then what is? 10000000 BCE?

Note, that I was already talking of relative oldness and did not refer to your post but to the comment of @WonderLand.

Due to the rejection of a Supreme God (Brahman), Atma and Vedas, Buddhism has actually left the umbrella of Hinduism, but it still falls under Indian Philosophy

@ruben2020 - It seems to me that in Hinduism Brahman is not a supreme God, This would just be a form of words. .

In Buddhism God is irrelevant. His existence or non existence doesn't affect the suffering that a being experiences here. Suffering is the problem that is caused by desire and attachment. Mind being the place where suffering is experienced, both Buddhism and Hinduism give the solution of controlling the mind through meditation to get rid of suffering and mental afflictions.
Yoga is just a process of ceasing the mental activities (yogaḥ citta-vṛtti nirodha - patnjali yoga sutra 1.2). It is only when the mind is active and thinking that any  feeling of joy or suffering arises. So through yoga and meditation the objective of calming and stilling the mind is achieved. Although Yoga was developed and preached by Vedic (Hindu) sages like Patanjali, it being just a physical process also practiced by Buddhists, just like we use cars or computers developed by scientists of other religion.
If you want a historical chronology then undoubtedly you can place Yoga system of Hinduism ahead of Buddhism. If you go through Vedic texts like Upanishads and Gita, which were available before the formation of Buddhism, then you will find mention of Yoga, meditation and other related practices. But in course of time both have influenced one another.
Regarding the relation between Buddhism and Hinduism my personal belief is Buddhism is Hinduism unnecessary parts casted out. While Buddishm primarily focuses on making life free of suffering here in the present life, Hinduism takes into account both here and the hereafter. Hence, while there are many yanjya and sacrifices prescribed in the Vedic religion for the hereafter, there are none such in Buddhism. The Upanishadic portions of the Vedas has teachings that are to some extent similar to the teachings of Buddhism. Both prescribe meditation as the mean to attain liberation. In fact message of Upanishads, Gita and other Vedic scriptures state that one who desires real benefit should not pursue sacrifices, yanjya, etc. as they provide temporary fruits in the after life and doesn't offer permanent liberation from material existence.
So the point is Yoga not being a philosophy (about which people can have different opinions) but being a physical solution to the problem of suffering is common and practiced both by followers of Hinduism and Buddhism. However, the point to note is that basically the meditation portion of Yoga are practiced by both, not the yoga asans or postures. Yoga postures and asanas are primarily practiced in Hata Yoga system which belongs to Hinduism.

just a notes: Patanjali didn't invent Yoga (2nd century BCE) ... as you said Yoga is mentioned already in the Veda (they are dated around 1700–1100 BCE beside it is consider to be an oral tradition that only 'recently' was transcribed to text ... so some people states veda are about 8000yo )

I agree 'Buddhism is Hinduism unnecessary parts casted out' but it depends what you mean with unnecessary because Veda contains information about Music/Art, Medicine, Psychology ( relation between Atman/Brahman, consciousness/universe  ) and the Universe nature itself ( it is a compendium of science) ... so I would say Buddhism only cover the psychology part analyzing the relationship between the world and the consciousness. So eventually we may also say that Buddhism is an extension of the Vedas. It may even considered a different path of the yoga.

Now this answer is about the historical development of Buddhism. In the mid of the last millenium BC there was a general movement in India, the so called Śramaṇa-movement. Cp. http://en.wikipedia.org/wiki/Sramana
It was an ascetic movement whose adherents strove to find liberation from this world and the cycle of rebirths by themselves and aside from the Vedic-brahmanic religion of sacrifice. The first literary witnesses of this movement are certain Upaniṣads, some of which the Buddha was also taught by the two teachers mentioned in the canon. One of the most important literary witnesses is the Sāmaññaphalasutta of the Pali canon.
A lot, actually most of the philosophical base of Buddhism was common sense of this movement. Even such a "totally Buddhist" doctrine as the Pratityasamutpada springs from this common source as can be shown by parallel structures (far less important and far less developed) in the Jaina canon and in the Manu-Bṛhaspati-Saṃvāda in the Mahabharata epic.
Now, to answer the question, apart from the person of the Buddha, there is IMO just one thing which singles out Buddhism as a movement of its own from the common ground of the Śramaṇas and that is precisely the theory of anattā or anātman. Up to the "mahayanic revolution" each and every philosophical development in Buddhism is already foreshadowed by this theory and these developments can quite consistently be seen as a fathoming of the hidden implications of that single tenet.
A note on dates:

It is quite well agreed that the oldest portions of the Vedic Literature are not older than 2000 BC or 1800 BC, rather younger.
The first Upanishads date from not before 800 BC, rather starting from around 600 BC
The Buddhas Parinirvana took place somewhen between 545 BC and 400 BC
Patanjalis Yoga-Sutras cannot reliably be dated, but it is unlikely, he lived before the second century BC

This makes Yoga younger than Buddhism.
Now, this was for the time, when Buddhism first developed. Until the time, that Buddhism nearly completely vanished from the scene in India, there were of course various influences from and to Buddhism, as has been pointed out in other answers.

good answer, but one quibble. Patanjali codified and systematized Yoga however Yogic practice itself predates his work - there is a school of thought its origins are pre-Vedic and quite likely it bloomed in the Sramana era.

Not too sure about Yoga. But I believe the core teachings of Hinduism are based on Nithya, Sukha, Athma. Which is the exact opposite of Buddhist teachings. So they are fundamentally very different. Hinduism is much more similar to Christianity and Islam at the core. Just that Christians and Muslims believe in one almighty God/Allah who takes care of everything, whereas in Hinduism the powers are distributed among at least 3 Gods: Maha brahma, Shiva, Vishnu.

Hinduism can be interpreted as form of monotheism as all Gods are basically different manifestation/projection of the Brahman (impersonal/neutral supreme self)

http://www.gitananda.org/faq/is-hinduism-polytheistic-or-monotheistic.html

Hinduism itself is not a monolithic religion. It is a spectrum of traditions from Monotheistic to Monistic to Polytheistic to non-theistic. It depends on which sampardhya the Hindu follows.

@Sankha Kulathantille, you are right that Nithya and presence of Atman are core to Hinduism but 3 Gods existing is not an essential Hindu belief. In Vedantic schools 3 Gods are not 3 entities but manifestation of the same single Nirguna Brahman who is eternal and outside the time, space & causal planes. Buddhism operates only within the causal plane, attributing every phenomenon to causes. As in my previous comment, schools such as Mimaamsa & Sankhya are non-thestic, i.e do not believe in a supreme creator God.

Yes, I've heard that too. But people worship them as different entities. The God concepts of Christianity and Islam are also outside the time, space & causal plane. It's wrong to say "Buddhism operates only within the causal plane". Nibbana is uncaused and that is the main goal in Buddhism.

You have tried to show the similarities between Hinduism and Buddhism (i am not talking about Yoga as I have not studied it much comparing to other two subjects. And also because I am doubtful about if it can considered as separated philosophy or religion.). In doing that you have talked about time period ( and similarities due to that) and about philosophical similarities - similarities in teaching.
In case of similarities of teaching we need to be little careful. There can be confusion due similarities of words. I will give just one eg. - you have talked about Karma. But Karma in Buddhism and Karma in Hinduism is very different. Plz refer to Buddha and His Dhamma.
In case of time period you are in other words saying that Buddhism is nothing but something build ed up on Hinduism. Again I have some doubts. This is mainly due the reason that Hinduism as such is very modern concept. There was Vedic time. But at that time various other philosophies were also present which were not strictly Vedic. And yes, as far as I understand Buddha derived lot from them as he was master in all those philosophies. It is surely different from considering Hinduism as base of Buddhism.
In case of differences, yes differences regarding presence of God are true. But we can not miss a major difference - Hinduism is highly dependent up on Varna system where as in Buddhism there is no such system, in fact, Buddhism is against any such system of gradation.
With all this, I have expressed my concerns regarding mixing Buddhism with Hinduism or reverse or saying that they are on same lines. For me Buddhism shares adverse relationship with Hinduism. It it the great religion of "Maitri" which is against any division between human beings on the basis of there birth. It is this aspect that a person who is approaching to Buddhism (especially from Hindu fold) should know.
Thankful to you for raising such important topic that helped me to express. Looking forward for further discussion on the points I have mentioned.

thanks you for your answer, I think it is very clear and centered the point.

I think some misunderstanding are present in my question because I start to doubt we can speak about Veda school and Hinduism as they are the same thing ... for example 'Varna system' has been implemented by the Hinduism but I am not sure Veda text speak about the requirements to divide the society in cast ... for ex Advaita vedanta (non dual) is one of the main Vedic school and it states Bhramam/Atman are the same and every division is an illusion ... so I don't see why a tradition that states division is an illusion should promote a cast system

We cannot find truth by studying and making comparisons among those so called scriptures of different theories time experienced , we have to experience our own doubts with humble and gentle    self precipitation, which needs very innocent and Self ignited mind , as an individual entity.

Hinduism flourishes after buddhism.. buddhism is history of india till mauryan empire i.e. 185 BC.. then hinduism entered into india through brahmins..
For more about this historical perspective follow this man (https://m.facebook.com/rajendraprasad.singh.509?tsid=0.6038788693962907&source=result)
But what i want to put here that hinduism being later to buddhism is bound to get influenced by it..that's why we see similarity between buddhism and hinduism.. hinduism in its philosophy has nothing to give to us..they all have copy pasted their philosophy from buddhism.
Only contribution of hinduism is that it has abundant of mythological story, lots of god..
But when it comes to moral,philosophy teaching hinduism is somewhat similar to buddhism..i may go to extent of saying , that because hinduism copied many of it, thats why gradually buddhism declined in india ..even the name of buddha is forgotten in india..ask the villager of india who is hanuman and they will easily answer. Ask who is buddha and they are clueless..but if there were no buddhism , hinduism will not be there as philosophy

Yoga asana can be very harmful to Buddhist practise because yoga asana can distort the way the body naturally breathes (which will actually hinder the development of right samadhi).

Reincarnation is not accepted by Buddha because he denied the presence of eternal soul. The core of Human being is not a soul but the mind. Mind and the body is undergoing through constant change and that's why rebirth is also occurring moment to moment. Reincarnation and rebirth are different if you try to understand in depth.
Doing meditation to reach enlightenment is Shraman (eg. Jainism, Buddhism) tradition and not the  Hindu or Vedik tradition.
Jainism is not started after Mahavira Jain and Buddhism is not started after Siddhartha Buddha. There were several Buddha before Siddhartha Buddha.
Hindu religion is mixture of all the tradition and religions and it is  newer than Buddhism and Jainism.
Buddha did not hide anything about God. According to him there is no God.
Karma theory is part of the Buddhism and it is not mentioned in Vedas. Bhagwat geeta is copied from Buddhist text and Bhagwat Geeta is not even part of the Original Mahabharata which has Krishna in that.
Proof of Buddhism being older that Ramayana is the presence of Buddha in Ramayana where Rama condemns Buddha for being Atheist. And Hindus says that Ramayana is older than Krishna.
Moreover Ramayana and Mahabharata are taught as Indian Mythology and  they are based on fictions.

As they were sitting there, the wanderers of other persuasions said to them, "Friends, Gotama the contemplative describes the comprehension of sensuality. We, too, describe the comprehension of sensuality. He describes the comprehension of forms. We, too, describe the comprehension of forms. He describes the comprehension of feelings. We, too, describe the comprehension of feelings. So what is the difference, what the distinction, what the distinguishing factor between him and us in terms of his teaching and ours, his message and ours?" ... Maha-dukkhakkhandha Sutta

In short: There isn't any relation between the Dhamma of the Sublime Buddha and other, like mentioned doctrines. The Buddha rejected them in regard of leading to right release and most in regard of leading to higher as well. So if one would ask for relations one can only answer rightly: Their relation rests solvely on being not related. Yet, everybody is invited to gain relation with the Gems, as this Dhamma is ehipassiko, 'Come and see', requiring of course leave at first place. Once done, one would be able to confirm the said, yet it has to be taken on more or lesser confidence at first place.
Not common Creatives originated and not left back as such.

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


text:
What Buddhist texts describe the doings of syncretized Hindu deities?
Some Vedic/Hindu deities are recognized as being part of Buddhist cosmology. For example, Indra, who is the chief god of the Vedic pantheon, is syncretized into Buddhism as Śakra, which is another epithet of his.
In Hinduism, the exploits of Indra are described in doctrinal texts like the Vedas and the Puranas, as well as in literary texts like the Mahabharata. But Buddhists (of any school) don't accept these texts as part of their canon, right? So, my question: in what Buddhist (canonical) texts would the doings of syncretized Hindu deities like Indra/Śakra be described?

Sakka appears in quite a few jātaka tales in the Theravada canon, including (from the last 10) the Nimi,  KhaNDahāla, VidhurapaNDita and Mahā-ummagga jātakas.

Malalasekera's Dictionary of Pali Proper Names is a great place to find this sort of information; for instance, the entry on Sakka has a whole list of sources for info on the entity, both canonical and commentarial.
On the other hand, I can't think of any other divine beings that have been expropriated in the same way as Indra; in fact I'm not sure expropriation is the proper term, since Indra just means "chief", and so it could just be the Buddha using the Hindu name to describe Sakka.
Edit: Yama shows up in the Devaduta Sutta (MN 130)

Wow, that is an excellent resource! (re: other Hindu deities - there's Yama, at least. I know that Shiva somehow made his way into Japan as Daikokuten, but I don't know what the exact chain of transmission was there. He doesn't appear to be in that dictionary, though; perhaps because only the Vajrayana schools syncretized him?)

Huh, didn't realize Yama was Hindu. He shows up in the Majjhima Nikaya... let me find the source.

I mean in the Jataka tales there is a clear reference to Hindu deities. A good example is Jataka 454. Also, this site which I am assuming is Buddhist mentions references to Vishnu as such. http://www.virtualvinodh.com/writings/assorted/vishnu-buddhism

@yuttadhammo Yama is the Hindu god of death yes.


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Nibbāna in The Progress of Insight
I was wondering if anyone could help to clearly explain the phenomenology of what happens in this passage from Mahasi's The Progress of Insight, specifically the bolded section:

12. Insight Leading to Emergence
So, through knowledge of equanimity about formations, which is endowed with many virtues, blessings, and powers, he notices the formations as they occur. When this knowledge is mature, having become keen, strong, and lucid, on reaching its culmination point, it will understand any of the formations as being impermanent or painful or without self, just by seeing their dissolution. Now that act of noticing any one characteristic out of the three, which is still more lucid in its perfect understanding, manifests itself two or three times or more in rapid succession. This is called "insight leading to emergence."

I am interested in all the phenomenology but I am especially interested in the part that says "two or three times or more in rapid succession". Does this refer to mind moments or what?

Are you talking about the book from Mahasi Sayadaw?

@Jakob Yes; from here: http://www.accesstoinsight.org/lib/authors/mahasi/progress.html

This passage is according to the abhidhamma treatment of the attainment of nibbana. The two to three mind moments (yes, that's what it means) are called anulomañāṇa ("anuloma~naa.na") - knowledge of conformity, the twelfth stage of knowledge.
The Visuddhimagga (XXII.128) describes this according to the abhidhamma:

128. As he repeats, develops and cultivates that equanimity about
formations, his faith becomes more resolute, his energy better
exerted, his mindfulness better established, his mind better
concentrated, while his equanimity about formations grows more
refined.
129. He thinks, “Now the path will arise.” Equanimity about
formations, after comprehending formations as impermanent, or as
painful, or as not-self, sinks into the life-continuum. Next to the
life-continuum, mind-door adverting arises making formations its
object as impermanent or as painful or as not-self according to the
way taken by equanimity about formations. Then next to the functional
[adverting] consciousness that arose displacing the life-continuum,
the first impulsion consciousness arises making formations its object
in the same way, maintaining the continuity of consciousness. This
is called the “preliminary work.” Next to that a second impulsion
consciousness arises making formations its object in the same way.
This is called the “access.” Next to that a third impulsion
consciousness also arises making formations its object in the same
way. This is called “conformity.”
(Path of Purification)

The next thought moment arising after these three takes nibbaana as an object.
EDIT: In plain terms:
Through the gradual understanding that all formations are impermanent, suffering, and non-self, the meditator attains an absolute certainty of one or another of the three characteristics and this leads to a release based either:

signlessness - based on impermanence, that there is no telling what will happen in advance; e.g. the rising and falling of the abdomen suddenly speeds up;
desirelessness - based on suffering, that there is no benefit to clinging to any formation; e.g. the rising and falling of the abdomen suddenly feels unbearable;
emptiness - based on non-self, that all formations are void of self and there is no relationship of ownership or control in regards to all formations; e.g. the rising and falling of the abdomen appears to proceed automatically without interference from the meditator.

This realization lasts two to three thought moments, during which the mind realizes the truth of suffering and discards the truth of the cause.
The next thought moment is an experience of cessation, where there is no arising of sense experience (including mental sense experience). This is the realization of path consciousness (the noble truth of the path) because it has the power to destroy fetters and therefore lead to freedom from suffering. It takes nibbāna as an object.

Thank you, Bhante. This Visuddhimagga passage uses a lot of conceptual language; I was hoping to get a phenomenological description in everyday language if possible. I realize, however, that a technical description may be required, to some degree, to explain this.

Edited to add a practical description.


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Hamstring issues when in a five-point-meditation posture
Most days when I sit in a five-point meditation posture on a cushion there isn't a problem when sitting for the duration of a meditation session, but for particularly long sessions or on some days, sporadically, my left hamstring will start to feel uncomfortable tight to the point where I will not be able to continue meditating through it. Usually when this happens can't even mindfully adjust to a position where it won't dominate the session from that point onward.
The pain is sharp and gradually builds until about all I can do is stretch it out and leave it that way. It appears to be muscular in nature. There are no medical conditions that I have that I am aware of that would lead to this problem, and there don't appear to be any circulation issues.
What are some of the elements I can ensure, adjust, do beforehand, or do regularly to try to keep this from happening or mitigate the problem?

This is a test of one edge of the type of questions I envisioned when I asked http://meta.buddhism.stackexchange.com/q/1/32

Maybe the desire to adhere to a particular meditation posture is the problem. If someone got it into their head that to meditate properly, one needed to hold a headstand position, then there's sure to be lots of discomfort to get in the way of the meditation.
The purpose of the posture is to reduce bad mental qualities that get in the way of meditation, things like back pain from slumping and not sitting up straight; things like lethargy that comes from lying down.
Yet you need some kind of relaxation to prevent giving the mind food for discursive thought. You can't really meditate while driving because there's too much to be responsible for, not enough room for the mind to calm down.
So how comfortable do you need to be before you can settle down? Is it a distracting thought or a legitimate injury you're doing to yourself? If your legs hurt when you sit down, then just stretch them out and go back to the breath. Yet if you find there's a constant, never-ending stream of uncomfortable things that you need to keep "fixing", then that points to a mental discursiveness that you need to stop following.
The Buddha gives ways of dealing with Distractive Thoughts. If all else fails, press your tongue to the roof of your mouth and batter through your mind's urge to "fix" parts of your posture.
(Re: closing the question, I think there are perfectly Buddhist ways to answer a question like this--these are distractive thoughts, although one needs to discern the difference between a mere thought and an potential injury which is yours to prevent. I've read stories of people injuring their knees because their teacher told them to keep sitting in tight postures, ignoring their pain.)


text:
How to help non-Buddhists understand a young person's desire to be ordained as a monk?
Many non-Buddhists do not understand the appeal or the benefits of becoming a monk. They may not be able to understand why one would want to live such a simple life, and they may not take the decision seriously.
What are some of the "selling points" for ordination (particularly as a young person just over 18) that a non-Buddhist would understand? Are there any organizations or resources for non-Buddhist families or friends of Buddhist monks (aspiring or otherwise)? How can one help a non-Buddhist loved one understand one's desire to be ordained?

Selling Points
According to the Buddha's teaching in the Samaññaphala Sutta (DN 2), there are a whole host of benefits to the life of a samana (i.e. a monk). In brief:

Freedom from requirement to engage in secular society (social engagements, civic duties, etc.)
Freedom from requirement to engage in secular employment (living as a mendicant means no need for money, etc.)
A blissful state in the here and now (through a moral code, sense restraint, and tranquility meditation)
Wisdom and understanding about reality (through insight meditation)
Supernatural mental abilities (astral travel, reading minds, remembering past lives, etc.)
Freedom from mental defilements of greed, anger, and delusion (through the attainment of nirvana)

I think that about sums it up better than I ever could :)
Resources
Normally a monastery would be the best source; often for Westerners intending to traverse the globe to ordain, that isn't as easy as it should be.
The Internet has some resources on monkhood for lay people, at least in the Theravada tradition. Here's a couple:
http://www.accesstoinsight.org/lib/authors/ariyesako/layguide.html
http://www.buddhanet.net/e-learning/buddhistworld/layguide.htm
Coming To Terms
For my parents, actually practicing the teachings themselves helped somewhat; once they understood the benefit of meditation, they were better able to accept what I was doing. Of course, it was only once I'd ordained and they saw how it wasn't really a brainwashing cult that they really opened up and actually appreciate it.

Thanks a lot for your help! I will try this for my parents, but I'm afraid they are not open to that since my dad at least is an almost fanatic materialist. May you progress on your path!:)

You're welcome :) I feel for you. Materialists can be terribly obtuse when it comes to the mind. Ask him about the "hard problem" :) http://en.wikipedia.org/wiki/Hard_problem_of_consciousness

Thanks again. I've just had a discussion with my parents and now things got even worse. They say by being a monk one just gives away responsibility and lives a life which is easy and comfortable. Instead I should serve society and play my part in the world. Doing otherwise would be very egoistic, only relying on others (and their donations). Sadly, they now think that I am part of a sect, which makes them even more averse to learning some meditation. They don't believe that I know what "is good" for me and say that I would be wasting my potential. I still have some time to talk with them, but

this is very likely not to lead to anything. Is it better to ordain without permission of the parents than not doing it at all? I appreciate your support!:)

Check out: http://www.bps.lk/olib/wh/wh110-p.html It took me two years to get my parents grudging permission. Good luck :)

Yutta, you're going to kill our 2.5 answers per question if you keep answering things so completely.

I'm not sure if that's a serious complaint, but we're already over 2.5, so shouldn't be a problem; i'm not answering all the questions :p

(Just finished the translation of a talk on respect, confidence and patient, for today, my person came accross this question here)
To those seeing the danger in the world, and those who might possible develop deep regard for them, going to strive to get beyond that:
Such as to find understandig, that one prefers to be just a alms-beggar, at least, is not easy to understand, especially if coming from a fortunate seeming sociaty, but it's not different in traditional countries, when it goes to really leaving home, and not just from home to a certain known monastery.
One, if serious, must be clear, that he might no more have any relative support but needs at least relay totally on his actions and cause and effect, trust the existence of goodness and a still present supportive reputation of the three juwels.
It's merely seldom that even friends, relatives incl. parents will easily have understanding or tolerance in regard of going forth, since one/you is/are regarded as a part of their own, a source of "food" for the sense, an object for identification for them, which gets of it's nature lost by 'changing' the family, or inspire such.
My person guesses, that the most proper comparison, for others to understand, might be with a warrior, going out into battle for a good for himself and all his kind. The case that in this case the battle is not fought outwardly, without weapons, and the death rate in battle is merely very small, might be a picture for reasoning for others who possible would understand why someone becomes a soldier, for example.
It's how ever not really possible to make others understand clear and it's a bliss to be possible surounded by people who actually understand a strive for deathlessness, it is a bliss if one even grows up in a family where the three juwels are regarded and the going forth and renouncing the world is praised.
In circumstances of even slight appearence of the luck and fortune of avaliable condition for such, outwardly like inwardly, it is wise to take upon this seldom appearence, which will be faster gone as the most think, even generally in this world.
Is worthy to point out again, that it is not a matter of ones relatives or parents birth, culture, raw believe and it's totally independend of geography but a matter of faith, not only in such a way, but also in you as person or better your tendency, to make and follow aspirations serious and eager, while not losing an eye on virtue and harmlessness for those around you.
So if not having developed and shown certain attidutes of a warrier, even a noble one, in your sphere till today, such to start on, would be possible the best way to gain the, or more fearless leave from those your are related for now. To progress it lesser in a merely argumental way can never be that effective like a presenting by deeds.
In this way, those words might be not only an encouragement for those with merely open doors for now, but also for does, not having the conditions yet, not to search for the enemy of ones aspirations outwardly and in the cultur and sociaty, but in ones own qualities and the need to cause ones supportive gained effects by oneself and work on it.
Once leaded a soon heading discussion about the matter of condition (Nissaya), strong condition (upanissaya) and strong condition cause (upanissayapaccaya), it maybe gives additional food for wise thought: Why it is important to value our Conditions?
[Note: This is a gift of Dhamma, not meant for commercial purposes or other low wordily gains in trade or exchange.]


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Can someone explain about children monks?
I've seen pictures online of young children dressed in monks robes in Buddhist countries. Does someone make the decision on behalf of the child that they will become a monk? Do they eat only one meal a day as adult monks do? Are very young monks also called Venerable Sir? Thanks for helping a western mind to understand this matter.

In Thailand, male novices (called nen or samanera) are a fairly common sight.  Very often they have taken vows only temporarily.  They may do it during the phansa (rainy season) period, during summer holidays from March to May, or just for a few days in order to make merit when a parent or grandparent has passed away.  The latter motivation is in a sense repayment of a debt owed to family members for being under their care as a young child.  According to Thai wikipedia, novices should be no younger than 8.  A temple website states that they follow only 10 precepts.  A Thai friend of mine told me that one motivation on the part of parents is that since the boys learn the basics of meditation practice, they are more mature and exhibit fewer behavioral problems when they come out.  I recall reading something like this in a biography of one well-known Thai monk – it might have been Buddhadasa bhikkhu.
Regarding language, my friend said that some of the special monastic vocabulary (like chan for ‘to eat') is used when speaking to novices as well as monks, but that the overall politeness level is less formal (e.g. novices are not addressed as ‘venerable’.)
In Burma I have seen young girls (samanerī or the Burmese equivalent) in pinkish robes out on alms rounds, perhaps later in the morning than monks.  You wouldn’t see that in Thailand though.
Donald Swearer discusses additional motivations for ordaining as a teenager in his book ‘The Buddhist World of Southeast Asia’ (1995), p. 48:

In Thailand one of the principle reasons for being ordained is to acquire an education.  Among poorer families often children cannot afford to attend school.  Ordination as a novice provides for their material needs as well as a basic education.  Indeed, if a boy is bright and highly motivated he may complete secondary school as a novice or monk, graduate from a monastic college, and then earn an advanced degree from a university in another country, such as India.  After teaching in a monastery school for several years or serving as an administrator in a larger provincial monastery he will probably disrobe and take a responsible and respected secular job.  Although such exploitation of the monastic educational structure siphons off able leadership, it has become standard practice and bears little or no social stigma.

I have known several university teachers who followed this career path - they were all from the relatively poor northeastern region of Thailand.
Swearer goes on to suggest that in an earlier era, ordaining at the age of puberty was a kind of rite of passage that all males went though.  Monks in fact lead rather comfortable lives and for a child from a poor family, being a monk would mean raising one’s economic and social status.  Given the traditional link between education and the sangha, it should be no surprise that males ordain at a young age and that this is encouraged by local cultural norms.  In comtemporary Thai society the link has been weakened with the advent of universal secular education, but elsewhere in Southeast Asia (Cambodia, Laos and Burma) it is likely still quite strong.

Thank you both for putting this in context. Under the circumstances, it seems like a pretty mutually beneficial system.

Who decides:
Often they are coerced into doing it for a short period of time; other places poverty drives them to ordain. In rare cases they do it of their own volition because of some wholesome supporting condition.
Eating:
Monks can eat technically eat two meals as long as it's in the morning hours from dawn to noon. Most monks fall into that schedule. Samanera (novice monks, usually under 20 years of age) often break this rule, eating in the evening, even though it's against the rules.
How they are called:
It depends on the country. In Sri Lanka, some samanera never actually become bhikkhus (fully ordained), so there is a tendency to call them all by the same honorific. In Thailand they are called "nen", as opposed to "pra", and they only wear two robes instead of three. I don't think there is a case of a samanera being called Bhante, which would be the equivalent of "venerable sir" in the Pali. From a monastic point of view, they are still considered unordained, and they only keep ten rules.

Householder Robin, interested,
Thanks for helping a western mind to understand this matter. is a good approach, Sadhu.
Thousands of gifted young people have anew ordained the last days in traditional countries and will enter their first Vassa, rains, tomorrow, dwelling good time near the tradition of the Noble Ones, take on follow the Arahats.
Today, sort entering a near monastery, my person was approached by a young Venerable who did many years as lay attendance service for the Venerable there, yount and old, now himself most joyfull and proudly monk, here still as Upasaka, guiding to Venerables to the remote cave.

Does someone make the decision on behalf of the child that they will become a monk?
A young person, "child", may develope such desire for himself and ask his parents for allowing leaving home and join the near of the Sangha.
Parents may encourage their children to live a life in the near of the Sangha and renounce. How ever, althoght not always the way, the child himself, at least formal verbal, has to ask a Bhikkhu for going forth under the Tripple Gems.
The cases of allowance by the Buddha to accept younger are often related to devoted followers children, also cases where those became orphans and tended to seek refuge under their parents near monastic teacher.
There have been also cases, at the Buddhas time, today as well, where parents seeked for a pleasing, secure life for their children and such use, for just educational purpose and later good conditions for lay-life are often the reason why children are send to train as novices. Some also dedicate one child for the religion, some take it as way out of poorness. There are as many ways and reasons as there a Novices.
In traditional countries, at least till some years ago, it was usus to get a while ordained as monk in the youth, at least to prevent the tradition and gain good behaviour in speech and body, learn the broad ways of good respect and conduct.
Some origin stories related to ordain younger people, children, from the Mahavagga:

Mv I 36: Upālidārakavatthu — The Story of the Boy Upāli
Mv I 37: Ahivātakarogavatthu — The Case of Plague
Mv I 41: Rāhulavatthu — The Case of Rāhula

Do they eat only one meal a day as adult monks do?
Technical they could eat from sun-rise till noon. Meal in the morning and short before noon are usual provided and prepeared. There are such as "medicine" allowed nourishments and it would not be of disadvantage bodily in most cases.
Are very young monks also called Venerable Sir?
Yes! Venerable Sir, Bhante,... One sould be clear that such even young person could be a holy men, even an Arahat. Even parents, family, friends... would never be dare to not, at least by speech and body gesture, regard the young as sublime and worthy of reverance person. Even the King would sit lower and bow down (of course if not just behaviour like village children). Other monks would address them as well proper and diverent to lay people.
Only the meditation focusing branch within the Mahanikaya Bhikkhus (incl. the western famous Ajahn Chah groups), those not well informed in Vinaya, tradition and dangers, would not highly regard homeless under the Tripple Gems, just regard them as kind of slaves, good branches of the Mahavihara branch as well as the Dhammayut branch act very careful and Dhamma-Vinaya regarding. For lay-people there is no difference in regarding at all, and even in the times of the Buddha lay people criticized those Bhikkhus not looking after their "sons" in proper ways, not to speak about the Buddhas rebukes toward them.

from the Dahara Sutta: Young
..."There are these four things, great king, that shouldn't be despised & disparaged for being young. Which four? A noble warrior, great king, shouldn't be despised & disparaged for being young. A snake... A fire... And a monk shouldn't be despised & disparaged for being young. These are the four things that shouldn't be despised & disparaged for being young."
That is what the Blessed One said. Having said that, the One Well-Gone, the Teacher, said further:
You shouldn't look down on
      — for being young —
  a noble warrior of consummate birth,
  a high-born prince of great status.
  A person shouldn't disparage him.
For it's possible
  that this lord of human beings,
  this noble warrior,
  will gain the throne
  and, angered at that disparagement,
  come down harshly
  with his royal might.
  So, guarding your life,
      avoid him.
You shouldn't look down on
      — for being young —
  a serpent you meet
  in village or wilderness:
  A person shouldn't disparage it.
As that potent snake slithers along
      with vibrant colors,
  it may someday burn the fool,
  whether woman or man.
  So, guarding your life,
      avoid it.
You shouldn't look down on
      — for being young —
  a blaze that feeds on many things,
  a flame with its blackened trail:
  A person shouldn't disparage it.
For if it gains sustenance,
  becoming a great mass of flame,
  it may someday burn the fool,
  whether woman or man.
  So, guarding your life,
      avoid it.
When a fire burns down a forest
  — that flame with its blackened trail —
      the shoots there
      take birth once more
  with the passage of days & nights.
      But if a monk,
  his virtue consummate,
  burns you with his potency,[1]
  you won't acquire sons or cattle
  nor will your heirs enjoy wealth.
  They become     barren,
              heir-less,
  like palm tree stumps.
So a person who's wise,
  out of regard for his own good,
  should always show due respect
  for     a serpent,
      a fire,
      a noble warrior with high status,
  &   a monk, his virtue consummate.

At least a inspiring, living,  Khmer folk tale "The story of Bhikkhu Sok"
Some stories possible inspire rejoicing with merits:

Einweihung von zwei jungen Novizen - Ordination of two young novices DEVATUTAS
Einweihung eines Samanera - Ordination of a Samanera (Ayung 01/2016)
Maha Mangala Sutta - មង្គលសូត្រ khmer Rezitation, blessing for you from Ven. fellows, for their ancestors dwelling in modern world in the internet (2014).

...9. "Patience, obedience, meeting the Samanas (holy men), and timely discussions on the Dhamma — this is the highest blessing....

A possible extended and revised answer, as well as given place for discussion and going more into it, can be found here: [Q&A] Can someone explain about children monks? How to regard young Samaneras?
Anumodana!
(Note that this is not given for trade, exchange, stacks, entertainment and akusala deeds, but as a share of merits and to continue such for release)


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How concerned should Buddhists be with the actions of others?
Even as I find peace and contentment in observing the 5 precepts and following along the 8 fold path, I realize I sometimes unintentionally benefit from those who don't live in this manner. For example  a friend takes something that wasn't freely given and shares it with me or a nearby person kills the insect flying around that I was trying to ignore. If I have not encouraged people to do such, should I be concerned about their actions or remain concerned only with my own intentions and actions?

I'm glad you asked this question as this came up in my life recently. I was marveling at a huge group of ants gathered on my brother's porch. This inspired him to grab a can of Raid and spray them all to death. I felt awful because I'd inadvertently caused hundreds of deaths. I'm still trying to figure out how best to avoid this type of occurrence in the future. Do I simply keep my enthusiasm and scientific curiosity to myself?

One option is to look at such situations as motivation for renunciation.

I am going to quote Jack Kornfield's Living Dharma, specifically the interview portion with Achaan Chaa, excerpt from the question of "If putting everything together in our bowls is important, why don't you as a teacher do it yourself?" (page 42 to 43 of my edition):

Wisdom is for yourself to watch and develop. Take from the teacher what is good. Be aware of your own practice. If I am resting while you must sit up does this make you angry? If I call the color blue red or say that male is female, don't follow me blindly.
[…] If you watch others at most ten percent of the time and watch yourself ninety percent, this is proper practice. […]
Looking outside the self is comparing, discriminating. You will not find happiness that way. Nor will you find peace if you spend your time looking for the perfect man or the perfect teacher. The Buddha taught us to look at the Dharma, the truth, not to look at other people.

So I would say that, based on this, the lesson here is to remain focused on your own intentions and actions, but to strive to fully notice your own reactions to what happens. If someone else kills the insect and you benefit, how does that make you feel? How do you respond to it?
I would argue that goes even if you have encouraged them not to do it.

There is no benefit to accrue to anyone except personal actions that lead to the ending of suffering.
Someone killing a pest doesn't "benefit" you, it gives you some short-term sensual pleasure--the pleasure of being outside and feeling a cool breeze without a determined gnat landing on your face. Or the pleasure of eating food/drink without having to pay for it. But these are certainly not permanent pleasures, nor ultimately fulfilling.
Instead of worrying about who did what action and what pleasure resulted, try thinking about why you think superficial pleasures like these are beneficial? So long as a mind thinks these are good things worth pursuing, it will pursue them.
And for the comment underneath you, also about killing insects:

I felt awful because I'd inadvertently caused hundreds of deaths

Something to think about: if you can't accept the death of an ant, how will you deal with your own death, when it comes? Think about the hatred or egotism that causes a person to kill ants and how it should be abandoned, don't think about how awful death is and how it should be avoided. Nothing anywhere is avoiding death and it's happening on a much grander scale in nature than it is with cans of Raid.

How does one prevent the killing of pests such as rodents, cockroaches, etc?

One aspect of Karma is that it is contagious nature and cumulative in nature. Say you have bad Karma; when the fruit ripens, in many cases some being near you should harm you and be instrumental in the karma giving its fruit. Then the being who is instrumental accumulated bad Karma. In the future some one else (in most cases) must be instrumental in giving a means for the karma to manifest.
Also due to the liking (or the lack of it) most people tend to be born together in Samsara with a higher degree of probability.
Hence if people around you do negative karma, then there is a possibility that there will be a negative vibe with all associated people due to the complex interactions.
Hence it is best to encourage your circle to be as positive as then can and avoid negativities but the best extent you can. This give two benefits:

Good Karma for you for doing a good deed
Collective good Karma (or lack of bad Karma) means you would accumulate more positivity through the process

Also being collectively good or doing good deeds as a group has better results than just doing as an individual.

@Robin111, this is a great question and a turning point from "Hinayana"-type-mentality to "Mahayana"-type-mentality (note: I'm not speaking about the schools Theravada and Mahayana, as both of these two types of mentality can be found within both Theravada and Mahayana schools).
The practice of transcending one's ego involves continuously reflecting upon one's actions and choices to see if they are biased with ego perspective. As this practice is refined, you may find yourself finding egoistic motives in seemingly egoless choices and vice versa. This is normal and good. Keep going until the end ;)

Isn't there a rule, about eating meat, something like,

Don't, if the animal would be killed specifically for you (e.g. because you asked for or paid for it)
OK otherwise (if you're begging for any type of food, and the donor chooses to give you meat)

A moral (i.e. a general lesson) that I read into that rule is,

Avoid being the cause of suffering; for example, don't encourage (pay money to) a butcher.
Optimize the situation which exists in the present; if the creature is already dead (through no fault of your own) and meat would benefit your body, then why not (waste not, want not)?

But I don't know. If for example that "friend or nearby person" were a child of yours, I think you should probably instruct them, to improve behaviour in the future: "Don't steal; I'd prefer you didn't kill; ...".
Trying to instruct an adult friend in way that might, I don't know, have negative consequences; so if you were to try to do it you should do so "skillfully".

One practice you might try in such a situation is use it as motivation to contemplate the unsatisfactoriness of samsara and resolve to develop true renunciation.
No matter what we do, as long as we are samsaric beings we are contributing to the suffering of others. Our very existence acts as a cause or condition for the suffering of others. The food we eat, the water we drink, the shelter we take... the basic factors we need to live all act as a cause or condition for others suffering.
This comment to your question was very poignant for me:

I'm glad you asked this question as this came up in my life recently.
  I was marveling at a huge group of ants gathered on my brother's
  porch. This inspired him to grab a can of Raid and spray them all to
  death.

This person had no ill will towards those ants nor took any non-virtuous action with regard to them and yet acted as the cause or condition for the death of those ants at his brother's hand. This is the predicament of samsara and I think closely related to the Sankhara-dukkha or the general unsatisfactoriness of this conditioned existence.
Contemplating like that might accrue to the cause of generating true renunciation for samsara.


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What does it mean to 'advert' to the factors of jhana after emerging from jhana?
I think this all comes from the Visudhimagga's explanation of jhana. I'm not sure there's any references to a term similar to "advert" in the Canon, but I keep running into the term advert without any further explanation in plain English of what that means, and it's a rare kind of word to begin with:

Following this the meditator should try to acquire five kinds of mastery over the jhana: mastery in adverting, in attaining, in resolving, in emerging and in reviewing.[16] Mastery in adverting is the ability to advert to the jhana factors one by one after emerging from the jhana, wherever he wants, whenever he wants, and for as long as he wants. ...

The definition of advert:

1: to turn the mind or attention —used with to <adverted to the speaker>
2: to call attention in the course of speaking or writing :  make reference —used with to <adverted to foreign-language sources>

Mastery in adverting means mastery in turning your mind to the jhana factors? So the first step of jhana mastery is the ability to turn your mind to:

applied thought,
sustained thought,
rapture,
happiness and
one-pointedness

--after you've emerged from jhana?
So after I emerge from jhana, I have to turn my mind to applied thought, then to sustained thought, then to rapture, etc. when and for as my mind wants to, no matter where I am.

I think you've answered your own question :)

In this context "advert" would mean to recall a cue that produces the desired effect.
For example in second jhana, to produce rapture and happiness without the use of applied/sustained thought, one may turn attention to the muscles of the face, temples, neck, shoulders, diaphragm, chest -- and recall the sensations they experience when feeling happy and joyful.
In first jhana, it would be recalling a particular idea (e.g. the happy fact that one is now separated from unskillful mental qualities due to having realized the Path).
P.S. I would not take "after emerging" literally. "After emerging" aka "post-meditation" generally means one's day-to-day practice outside of formal meditation.


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Days of Worship
I understand Buddhists don't technically worship, but pray to the Buddha or meditate (apologies for any mistakes). My question is: do Buddhists have a certain number of times a day to worship/pray/meditate? And is there a certain day/days out of the week they congregate together to worship/pray/meditate?

If one of the answers looks good to you, are you willing to accept it or provide feedback? ^_^

@Hrafn Yes I am willing, and I have just accepted an answer, it was just hard to choose they are all so good :)

There are Uposatha days, wherein one makes increased effort at following precepts (either being more conscientious of the five precepts or temporarily adopting the eight).
I gather that there is often more deliberate meditation or study as well on these days, in addition to precept following:

It is usual for lay people to go to the local monastery and to spend all day and night there. In different monasteries, of course, the way they spend their time will not be the same and much depends on which aspect of the Dhamma is stressed there: study or practice. Where there is more study, they will hear as many as three or four discourses on Dhamma delivered by senior bhikkhus and they will have books to read and perhaps classes on Abhidhamma to attend. But they are quite free to plan their own time with meditation, discussion of Dhamma with the bhikkhus and so on. In a meditation monastery lay people will get less instruction and that will be about the Practice of Dhamma, while most of their time will be spent mindfully employed — walking and seated meditation with some time given to helping the bhikkhus with their daily duties. So the whole of this day and night (and enthusiastic lay people restrict their sleep) is given over to Dhamma.
Lay Buddhist Practice

Then there are other various holidays and festivals. I'm not sure if any of the other holidays involve increased practice or not. Some seem like they would just involve paying respect to the Buddha (Vesak) or monks (Kathina Ceremony).

First of all, in your question, "but pray to the Buddha" is not technically correct, as we cannot "pray" (assuming the meaning of the "pray" as praying to external being ie, god) to Buddha (He is no longer here to listen to the prays). We pay respect to Buddha (, Dhamma and Sanga). However in a way I agree with you that some people actually "pray" to Buddha. I don't think it will result in any benefit, though.
OK, about the questions, according to my understanding and experience:

Do Buddhists have a certain number of times a day to worship/pray/meditate?

The answer is NO.

Is there a certain day/days out of the weak they congregate together to worship/pray/meditate?

The answer is Quite NO.
However, during the full moon day (in countries like Sri Lanka), we observer "Uposatha sil". In some cultures, this happens every week accordance with the four phases of the moon.
Anyway, in practice, when it comes to daily routine, we like to start the day by paying respect to Buddha, Dharma and Sanga and end the day by doing meditation at least for 5-10 minutes.
Further, when it comes to actual meditation, I think you can do it with most of your daily activities. You could do "breath meditation" when you are waiting to the bus, or do some walking meditation, when you are walking to your work etc.

Speaking from my experience with Western Buddhist communities: There is usually a day (or more) in the week where members of the sangha can meet and meditate together. But that is not a specific day, just when it is convenient for the organisers.

Would you be alright with being more specific about which Western Buddhist communities you have experience with? I think that would help make this answer more useful to future readers.

Parinirvana day is celebrated in my Sangha (Triratna) and I believe some East Asian Buddhist communities. It's the full moon that is nearest to the time of the Buddha's death or parinirvana.
The tradition goes that the Buddha attained enlightenment or nirvana when he was a youngish man (around thirty). He elected to continue as part of the world spreading the Dharma for another 50 years only achieving final release on his death - his parinirvana. I find this very evocative.
Anyway for us it's an opportunity to re-engage and deepen our practice. To really get stuck in - with the other members of the community