Puzzle #1:
White should play 1.b4!
White will either win Black's queen, or checkmate Black with Rf8#.
In Puzzle #2: White no longer wins with 1.b4 because Black has 1.. Re1+
If White plays 2. Rxe1, Black plays 2.. Qxc3.
If White plays 2. Qxe1 Black checkmates White with 2.. Qb2#