2 Mates in 3
Sorry, but your first puzzle doesn't work.
After 1. Bd6, either BxN or c3+ prevents the mate.
Even KxQ as black's second move prevents the mate also . . .
I love the mate with the king surrounded by his own pawns! However, it's probably incorrect to call this a puzzle since the opposing player should normally play the best move in a puzzle. Black does himself in here - more like a check-help!
For the first puzzle, adding a White Bishop on d7 and a White Pawn on f5 fixes the problems. Then the solution is 1.Qd6+ exd6 2. Be6+ fxe6 2. Ne3#.
The second puzzle actually has a few different solutions. The alternate promotion, which was pointed out but would probably be OK as it doesn't change the intent or spirit of the puzzle, but also an alternate move order (2. fxe8=Q+ instead of 2. Rxe8+) and a completely different first move: 1. Qxf8+ Rxf8 2. Re8+ Rxe8 3. fxe8=Q(or R)#
It is absolutely impossible. There had to be a minimum of eight pawn captures by Black to reach the puzzles initial position, however white is only missing six pieces.