Archmage!

WHITE: K-g4; Pawns c4 e5; R-e8; B-h7; BLACK: K-e4; N-d4; Pawn f5; R-f8; Black has just moved its pawn from f7 to check the white king. White must respond and checkmate black in one move. Which move?
WHITE: K-a1; Q-d1; R-b3; R-f8; B-h2; B-a6; N-d5; N-h4; BLACK: K-f2; Q-f5; B-b8; White to move and checkmate black in one move. Which of the following isNOTthat move?
WHITE: K-h3; Q-h6; Pawns: g3 h4; BLACK: K-e5; Q-c2; Pawn: g5; Black to move and checkmate white in two moves. What is its best first move? (The best first move is the one which enables black to checkmate white in the second move! So you have to think forward from your choices given below and also consider how white will respond to your first move! If your choice is correct then black will checkmate white on the second move regardless of white’s response.)
WHITE: K-a2; Pawn g7; BLACK: K-c2; N-b1; B-a1; Black to checkmate (NOT stalemate!) white in two moves. What is its best first move? (The best first move helps black to checkmate white in the second move. So you have to think forward from the choices given below and also consider how white will respond to your first move! If your choice is correct then black will checkmate white on the second move regardless of white’s response.)