First of all: I don't understand your #2: 1. g2+ is an impossible move.
Concerning #1:
- Ng6 (it's no check, "+", by the way) Nxg6
- Rxh7 gxf6
- Rxf7 c5
- Rhh7
Now you mean that white will win with Rfg7# (not Rfg2)?
What will you play after:
- Ng6 Nxg6
- Rxh7 gxf6
- Rxf7 Nf4?
What will you play after:
- Ng6 gxh6?
How about:
1.Ng6
a)1...hxg6 2.Rh8#
b)1...fxg6 2.f7+ Kh8 3.Rh7+Kxh7 4.f8R or Q#
c)1...Nxg6 2.Rxh7 gxf6 3.Rxf7
c1) 3....c5 4.Rhh7 and white will mate with Rfg7
c2) 3....Nf4 4.Rg3+ Kh8 5.Rxf6 Kh7 6.Kf7! Nh5 7. Rh3 and mate next move with 8. Rxh7.
d)1....gxh6 2.Ne7+ Kh8 3.Kxf8! c5 4.Rg3 Qg2 5.Rxg2 and mate next move with Rg8.
You mean with 8. Rxh5? :)
.. and mate next move with 8. Rxh7.
You mean with 8. Rxh5? :)
Yes, I meant 8.Rxh5. Damned clerical errors :-)
d)1....gxh6 2.Ne7+ Kh8 3.Kxf8! c5 4.Rg3 Qg2 5.Rxg2 and mate next move with Rg8.
... h5 4. Rg3 h6, and now?
4.Kxf7 followed by 5.Ng6+, 6.Nf8+ and 7. Rg8 mate.
You mean 5. Kxf7. :-)
Right, or also 5. Rg8+ Kh7 6. Rg7+ Kh8 7. Kxf7 and then 8. Ng6#. :)
Yes, 5. Kf7 :-). I had it that way but corrected it ...it is too hot :_)
That's clearly enough to deserve a little upvote. :)