The king can move at any time as long as the square it goes to does not put it in check. If the king were to be put into check, it has three options:
1) Move from the square to a square where it isn't put in check.
2) Block the check with another piece (unless the attacking piece is a knight).
3) Capture the attacking piece.
Yes, the king can move out of check, provided that doing so is a legal move (i.e. does not move into check again). If it cannot and there is no other way to defend the check, then it is mate.
Uncovering the king and it's exposure to check is an illegal move .
No , if your king is in check you can not counter with placing your opponent's king in check - you must respond to the move on your next turn by dealing with your king in check by moving the king out of check , removing the attacking piece by capture or by blocking the checking piece or you will need to concede / resign from the game . Look to the related link below regarding the rules of chess .
Yes, the king may capture the piece that is checking it.Yes, but only if that piece is on a square adjoining him, as a king has mobility of only one square per move.
Yes as long as he isn't in checkmate or he cant move into another check.
Yes. If you have your opponents king under threat, you have to say check. If you have their king in a position to take it and they have no move left to save it, you say checkmate.No, you don't have to say check or checkmate. I used to play in USCF tournaments and we never did.
Yes, if the king is in check, the next move must take the king out of check. You do not necessarily have to move the king, you could take the attacking piece, or block the check by moving a piece in the way.
No. You may not move INTO check. If that is the only move available, it would then depend whether or not you are already in check. If you are in check and cannot move to a square where you are not in check, it is checkmate, the game is over, and you have lost. If you are not in check, but cannot move without going into check, and you have no other piece or pawn that can move, then it is stalemate, and the game is a draw.
No.
Yes.
If what you mean by "leaving your king open" is not moving it out of check if your opponent puts your king in check, then yes, that is an illegal move. If your king is in check you mustmove to protect it. If you mean simply that you leave your king in the center of the board without castling or other protection, then it is not an illegal move. It may (and probably will) result in your king coming under attack very quickly, however.
no he also cant move into check via castle