Nothing, if the king was knocked over inadvertently. The laying down of a player's king has come to symbolize that player conceding victory to the other player. It is symbolic only and has no meaning unless intended as a symbolic gesture of concession.
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Yes. If the queen moves within one space of the king, the king is technically in check. If no other piece covers the space on which the queen rests, the king may take the queen to resolve the check. A king can only take the queen if the queen is opposite color of the king and the queen is not guarded by another piece.
The king can never be 'taken' by an opposing piece. When the King is under threat from another piece, the next move must be to get it out of check, either by moving the King, or breaking check by interposing another piece in between King and aggressor, or by taking the opposing piece. If the check cannot be broken, then it is Checkmate, and the game ends.
A common gesture of surrender though, is to knock one's king over to decare you are resigning from the game.
That is not a permissible move. Your opponent would have to advise you that you can't do it. If you do it anyway, you lose. The game is over.