An Unprecedented Checkmate

This is a game I played a few hours ago which I won, so it looks like I am gloating over a victory I feel proud about, but after winning the game, it's hard to feel good about winning. This was a 5-0 blitz game, with opponent rated 1407 postgame.

What gives me mixed feelings is that: what I should have lost, due to a significant material deficit initiated by my own errors, I ended up winning, so I would like to ask some questions regarding this game:

1. During the second half of the game, was the move 24. Rb8?? the one move which costed my opponent the game? I am asking this because even though it certainly caused me to deliver checkmate, there might be a habitual mistake that ended up making this whole situation possible.

2. If my opponent had played 24. g6, then with decent play from both sides, would I have had a possible checkmate right then, or would I have basically been losing?

At the current moment, I don't have access to any computer analysis engines, so I would like human opinion on this.

Thank you very much, and apologies for a bad adjective in the title, I thought that word meant something of the form of doing without realizing.