Did I damage the breaker by incorrectly wiring a generator?
You probably overheated and burned every component in that line, including the wiring and the GCFI outlet.

You probably melted/decomposed the insulation on that circuit. The GFCI is tripping because you have significant leakage on the hot or neutral lines, which means they're leaking to either the ground or to some other path within the house.

You may have damaged wiring on other circuits in the house, even if they appear operational.

I don't think it's possible to burn out a breaker unless it was already defective. It interrupts the hot leg and has no grounding, so it has nowhere to short to, and will shut off it senses too much current, saving itself and whatever is on that circuit.