First of all: I don't understand your #2: 1. g2+ is an impossible move.

Concerning #1:

1. Ng6 (it's no check, "+", by the way) Nxg6
2. Rxh7 gxf6
3. Rxf7 c5
4. Rhh7

Now you mean that white will win with Rfg7# (not Rfg2)?

What will you play after:

1. Ng6 Nxg6
2. Rxh7 gxf6
3. Rxf7 Nf4?

What will you play after:

1. Ng6 gxh6?