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6

No, you may not ever move your king into a position in which it is threatened ("in check"). If you did, your opponent could just immediately capture your king, and you would lose. Reference from the FIDE Laws of Chess: 3.9. ... No piece can be moved that will either expose the king of the same colour to check or leave that king in check.


4

You can solve any such problem by pretending the rules of check and checkmate don't exist, and instead you just lose when your king is captured. In your case, if you take the pawn, black will take your king and you will lose. The rule of check becomes unnecessary since all it says is you can't make a move that allows your opponent to win immediately, and ...


1

Taking the pawn places your king in check, under threat from the opponent king. As white, you have no way of creating check on your opponent, let alone mate. White loses.



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