Analysis please!


You played very well for someone of your rating. I actually think 18. f4 was called for - you got a lot of pressure down the open f-file.
Also, if you'd played 25. Kf2 instead of Kh1, you'd probably have had a won position, since his king is exposed and you can swing the a1 rook over to g1.
On move 36 you had another free pawn on c5, and the a5 pawn also can't be defended. After taking those, your mass of connected passed pawns would have been unstoppable.
I probably would have played 46. Rg4.
You're right that 53. Ra3 would have won.
In short, you should have had more confidence in your position instead of going for simplifications all the time - you were ahead for most of the game.

41 Rh4#
You missed several wins. Of course, he did to. Failing to take your c4 bishop in the opening was inexcusable.
I always find rooks difficult.
They do well behind passed pawns. As you and gabriel mention, you could have done so. They also do well on the 7th rank and one of black's better moves was 46...Rc2.
45 Rg2 could have prevented that.
The problem I have with rooks (or even giving advice on them), is that the 3 places rooks belong, open files, 7th rank, and behind passed pawns are almost invariably contradictory. By which I mean: you put your rook on the 7th, he takes pawns on the 7th, and he winds up in front of and blocking the passed pawns he created.
Luck