He didn't return as Berserker to kill her. Servants don't choose their class, that's pre-determined by their legend and stats. To summon a Berserker class servant in Fate, you actively do so by adding lines to the summoning ritual and said servant must have been driven to madness at some point in their history. Kariya was instructed to summon Lancelot as Berserker because the Mad Enhancement would up his stats, to put him on par with other servants, due to Kariya being a weak magus and master.
To start, you need to look into some of Lancelot's tales. There are stories in Arthurian legend like where Lancelot is involved in an affair with Lady Guinevere. The the affair officially exposed by Sir Mordred and Guinevere is effectively put to the stake, Lancelot then kills several knights including Sirs Gareth and Gaheris of the round table in rescuing Guinevere. Lancelot then denounces his knighthood and goes hermit mode. All of this basically startsto the collapse of the round table, Mordred usurping the throne and the death of Arthur, etc. Throw in a few occasions where Lancelot goes mad (depending on the story): being tricked into fathering Sir Galahad by Elaine King and going crazy upon realising this, going a bit mad for blaming himself for Arthur's death and such. There's a lot to Arthurian legend and I can't be bothered with more than this. But that's the general jist of it.
Anyway, back to Fate and Berserker's reasons, because the Saber v Berserker fight was a whole load of different to the LN and they didn't cover the reasoning, so I'll just skip to the part where Berserker stops, with some omission:
"Yes… Thank you. Perhaps, this is the only way I can convey my longing.”
Looking upon the sword that pierced his body with a gaze filled with compassion, Lancelot smiled wryly as he continued to speak.
"Actually… at that time I had hoped that you would personally punish me. My King… At that time I really wished that you would denounce me out of your own anger…”
The traitor knight, Lancelot who was called the culprit of the split of the Round Table — thus he spoke with sorrow to his only friend, who had never blamed him even until the very end.
"If I could have been punished by you… If you had demanded recompense from me… Then I would definitely believe in redemption… I would definitely believe that one day I can find a way to forgive myself. … The Queen is probably the same…”
"To die in the King’s arms, before the King’s eyes… haha, like this it is really… as if I am a loyal knight…”
In short, Lancelot wished to be condemned for his actions, something that Arthur never did, so that he could also find forgiveness for his actions.
About the actual fight:
Post-Arondight, Saber shouldn't have really have fought back as she did, seeing Lancelot basically left her broken and unable to do anything more than deflect Lancelot's blows. The anime made it look like Berserker's death caused Kariya's death, when it was the crest worms running out of prana to supply Berserker causing him to halt, which allowed Saber to make the killing blow.
Not only that, Kariya is meant to live long enough to make it back to the Matou household, where he tells Sakura that he's come to rescue her... before dropping dead.
As for the grail debacle. It was the grail posing as Irisviel, with her being its vessel and that. It would have been more apparent if she was wearing the black dress she was supposed to be wearing, but I don't think it wasn't too hard to figure anyway. The grail, being corrupted, is a dick, as stated in previous Fate stories and earlier in Fate/Zero, it doesn't grant wishes in the expected way, it grants them in the ******** genie way: wish for a million pounds, go a 2 million in debt first. The grail explains this methodology to him with the boats. Kerry wishes to end all human conflict, the grail would do this by killing everyone in a fashion similar to the boat dilemma until it boils down to an equilibrium. It's also a roundabout way to also show Kerry's actual desire, to be able to live in peace with his family.