.. 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.