You can read the whole series here.
The location of Passion events is not certain. For Gethsemane, it’s obviously related to an olive grove, the name means oil press. It seems to be located near the hillside. Olive trees can live for millennia, but the trees that exist there now, are not those from Jesus’ era. When Titus was crushing the Jews at the end of the war in 70, he cut down all the olive trees around the Mount of Olives (Josephus mentions this specifically), he needed the wood and it removed any cover for fugitives. Present landmarks you might see on a tour of the area are merely guesses. About the only things one can say with some slight assurance is that the spot was near the base of the hill, the trees do much better in that area.
The Synoptics have Jesus praying at Gethsemane (John says there is a garden there, but Jesus does nothing there in John, beyond being arrested). The scene in the Synoptics is one that hosted a lot of criticism in the second century, and in fact the pagan critics of the era were quite observant. They mock the disciples as failing here, they fall asleep, they take off when the arrest happens, etc. Jesus was a fraud, he had no real influence as a leader. What kind of God do you have here? He falls to his knees and begs to be excused, he’s weak. They compared the death of Socrates to the death of Jesus. Socrates has to take poison, he encourages his followers that he’s going to a better place, a better life, they shouldn’t fear, all is well, etc., etc. Jesus on the other hand appears fearful, falling to the ground begging for relief. Critics found him a pathetic figure. And they counter Christian preachers, telling people, if you really like this stuff, why don’t you just be a Jew? They at least have a real tradition instead of this upstart.
The Gospels don’t really explain what’s going on here, that develops later with all kinds of explanations: Jesus doesn’t really fear for himself, he’s pondering, experiencing misery over the sins of mankind, etc. Paul works out much of this, and Luke does some in Acts.
When Jesus gets to the place of prayer, he asks the disciples to watch and pray, he takes Peter, James, and John a little further, then he separates from them, and goes on and prays alone. People wondered how his prayer could be narrated, when he was alone. Maybe he tells them after the resurrection, and there was some mockery that went on about it. But in fact Jesus talks about prayer during his life with the disciples. The episode is pretty easily filled in with traditions of how Jesus prayed. And we don’t get much about the prayers in any case. Hebrews mentions the episode as loud cries, supplication, imploring God (for relief? to divert what was coming? it doesn’t say).
In the days of his flesh, Jesus offered up prayers and supplications, with loud cries and tears, to him who was able to save him from death, and he was heard because of his reverence.[ESV Heb. 5:7; it’s quoting Psalm 22 again (vs 24).]
There is little to go on in terms of timing. While John doesn’t have the prayers here, he does do it in chapter 12:27-28. There are a fair number of parallels to the Lord’s Prayer here. In the Book of Mormon, Jesus models prayer and the text does this by bringing the New Testament in play. It takes all the Gospels (a significant portion of John) and gives a kind of reified crash course in Christian belief.
 The Book of Mormon echoes some Pauline tradition in speaking of Jesus praying: it can’t be relayed in human language, it’s too powerful, holy. But to the point, it also speaks of Gethsemane in prophetic mode, when an angel comes to the king and speaks about Jesus:
1 And again my brethren, I would call your attention, for I have somewhat more to speak unto you; for behold, I have things to tell you concerning that which is to come.
2 And the things which I shall tell you are made known unto me by an angel from God. And he said unto me: Awake; and I awoke, and behold he stood before me.
3 And he said unto me: Awake, and hear the words which I shall tell thee; for behold, I am come to declare unto you the glad tidings of great joy.
4 For the Lord hath heard thy prayers, and hath judged of thy righteousness, and hath sent me to declare unto thee that thou mayest rejoice; and that thou mayest declare unto thy people, that they may also be filled with joy.
5 For behold, the time cometh, and is not far distant, that with power, the Lord Omnipotent who reigneth, who was, and is from all eternity to all eternity, shall come down from heaven among the children of men, and shall dwell in a tabernacle of clay, and shall go forth amongst men, working mighty miracles, such as healing the sick, raising the dead, causing the lame to walk, the blind to receive their sight, and the deaf to hear, and curing all manner of diseases.
6 And he shall cast out devils, or the evil spirits which dwell in the hearts of the children of men.
7 And lo, he shall suffer temptations, and pain of body, hunger, thirst, and fatigue, even more than man can suffer, except it be unto death; for behold, blood cometh from every pore, so great shall be his anguish for the wickedness and the abominations of his people.
8 And he shall be called Jesus Christ, the Son of God, the Father of heaven and earth, the Creator of all things from the beginning; and his mother shall be called Mary.
9 And lo, he cometh unto his own, that salvation might come unto the children of men even through faith on his name; and even after all this they shall consider him a man, and say that he hath a devil, and shall scourge him, and shall crucify him.
10 And he shall rise the third day from the dead; and behold, he standeth to judge the world; and behold, all these things are done that a righteous judgment might come upon the children of men.
This text is not a completely biblical one in terms of its world view of illness, and it mentions evil spirits dwelling in the hearts of people, this is a curious intersect with Joseph Smith’s later cosmology, and it has the Lukan sweating of blood, and it has crucifixion! This should be seen as translation effect perhaps.