While it is true that the white pieces have more material, the black ones have a better position. After H4xH5 the first check comes and White's king must go to the square of G1, then Rook to H1 would come giving check again and the white rook would fall in B1, and it is better that White surrenders.
White is totally lost, the biggest disadvantage being the doubled pawns on the E and F columns.
I think you're right on this.
Well, nice to see that you play chess, too, but even if 1. ... Rxh4+ seems to be the obvious move in this position, that was not yet the correct solution. :)
Nice to see new people joining my chess riddles! :)
OK, lets look at your suggested moves (black's moves are always in the right column):
But now white can give a check with:
And it's white who wins ...
You need to find something better! :)