1. I think in live chess, to claim a draw on repitition, you need to press "draw" ( not sure on that one).
2. You can castle if you've been in check, you just can't castle if you've moved your king or you're castling through or into check.
Some Questions on Chess Rules
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For your first "rule" the position has to be exactly repeated 3 or more times. Also this isn't a stalemate, it's a draw.
For your second "rule" you can't castle if you have moved your king, the rook, or by castling move your king through check. You also can't castle to get out of check.
If the same position repeats three times on the board, with the same player to move, and all other conditions the same (allowability of castling, en pessant, etc), then a player has the option of declaring a draw. It shouldn't be automatic - one of the players has to realize it and declare the draw.
In the case of castling, you cannot castle out of check or through check, but if your king isn't currently in check, castling is ok, even if it was in check on a previous move. This of course assumes that all the other castling conditions are ok (nothing between the king and rook, neither has moved yet).
I played a few games in Live Chess today, and I noticed that somethings I thought were against the rules were allowed:
My opponent and I played the same 2 move sequence three times in a row near the end of a game. I thought when this happened the game automatically ended in a stalemate.
In the middlegame stage of another game, I decided to castle. But then I remembered that I had been in check earlier. I went to castle anyway, figuring it wouldn't let me, but it was allowed. I though that one of the rules of check was if you have been in check beforehand then you can't castle
I'm pretty sure those are 2 rules of chess, but maybe I don't know what I'm talking about. If anyone can clarify these rules, I would greatly appreciate it.