Answers 

1. Be6+

   1. Be6 +, KxBe6

   2. Qe8 + followed by d5 #

2. Qe3+

   1. Qe3+, Kh8

   2. RxBb7, KxRb7

   3. Bh6+, Kh8

   4. BxRc8 (white is up a piece and threatens mate with Qf6+ followed by Qg7#)

3. Kg7

   1. Kg7, h4

   2. Kf6, h3

   3. Ke7, h2

      1. If black plays …Kb6 instead, you play Kd6 and then push the pawn

      2. Playing 3. Ke6 is a mistake since: 3. …h2; c7, h1 = Q; c8 = Q, Qh3+ and black wins with a skewer to capture the white queen

      3. Playing 3. Ke5 is a mistake since: 3. …h2; c7, Kb7 and black can queen his pawn safely

   4. c7, h1 = Q

   5. c8 = Q