Yes, the king can take another piece to get out of check, but only to get out of check.
yes as long as killing the queen will not put you in check
Yes, it can, as long as it doesn't put the king in check. PS, it's "capture", not "kill".
Absolutely, as long as it does not put the king in check.
Yes and no. If the king is in check then you are in the position to kill it but, the other player must move him out of check. If the king is in checkmate, then you have won the game and the other player can't move.
Yes, as long as the move doesn't leave the King in Check from another source.
According to the rules of chess, you cannot move your own king into the check position.
Only in certain circumstances such as having your king in check with no squares to move to and the only way to stop the check is to capture the piece delivering the check.
Yes, as long as it doesn't put him in check.
by asking nicely! Check the instruction manual