Check and checkmate on following moves I was playing chess with a buddy, and I put him in check. On the following move, without moving his king out of check, he moved a rook to put me in checkmate. 

My questions are as follows: 


Can he do that and leave his king still in check?
Even though I'm in checkmate, can I take his king to win the game?
Is checkmate an automatic win (meaning no moves can follow), or can I still "try"?
If it was an illegal move, where do we resume?
No, this is not legal.
Not relevant since 1 is illegal.
Checkmate is a win and no moves can follow. 
You go back to illegal move and correct if its a friendly game, I don't know what the official rules are for when a player makes an illegal move.