Puzzle 7 solution

Here's Black's helping move, Gd8:

Here's White's reply, Gd6 mate: 

Puzzle 6 solution

Here's Black's helping move, g5:

Here's White's reply, Gg6 mate:

Puzzle 5 solution

Here's Black's helping move, g6:

Here's White's reply, Gf6 mate:

Puzzle 4 solution

Here's Black's first move, Gh8+:

 

Note: Red is the indicator that the player to move is in check. White has three legal moves, Bf8, Bd8, and Ka7. The bishop moves simply prolong the game by one move. Let's assume White's reply is Ka7. Here's Black's final move, Gc8 mate:

Puzzle 3 solution:

White mates with Gf7:

 

Puzzle 2 solution

White mates with Gg7:

Puzzle 1 solution

 Black mates with Gxf3: