Where can I improve?

White should have lost this game after he went a rook down. The mate threat was easily defended and it was just a blunder that allowed white to win/mate. 

I just stopped after Re1 :)

You have no serious weakness in your play (at your level), but in an online game, wrong calculation in a simple exchange that leads to material loss should not happen. It is a matter of how far you want/able to calculate (2.5 move ahead is I think a minimum).

I think you are good at attacking, hence one tip from me on attacking motif: You can open up a file in front of your enemy King and put a Rook on the file. You had a chance to do that with 14.Kh1 followed by 15.Rg1.

In your game, the g-file was opened by accident. At master level, you wont give away your double bishop like that (which caused the g-file opened), but at your level it is difficult to benefit from double bishop anyway (how to play it is not easy), so tactical consideration (such as attacking chance) is imo better than positional consideration (So it is okay if you want to open the file intentionally)

okay, prove it.

Positionally White has lost after 17...Rxe4. If you look at it, White is "only" down one pawn in material but notice that 4 of White pawns are now scattered (unconnected), not to mention the overexposed King.

Tactically White has to resign after down a Rook without compensation. This is where I told you that you should practice to calculate deeper, at least 2.5 move ahead (20.Rae1? Rxe1 21.Rxe1 Qxe1+ and you lose one Rook in a simple exchange).

Black can defend White's threat because there is a Bishop at b2. The blunder was 24...Ne5? blocking the Bishop from defending g7.

Black can OTOH checkmate White by attacking the King from behind (first and second rank) using Rook and Queen, and minor pieces and pawns from the other side.

Computers play really bad if you play a opening that it's not in it's opening book.