A Honda gen will keep running even after its circuit breaker is popped. You reset the CB by stopping the engine and starting over ( with the load unplugged), then plug back in with less load. If big load, start gen engine with eco off then wait till all running then turn eco on or the engine might conk out at first.
A GFCI will not reset unless it has power. Yours acts like no power, so concur with previous idea, that the gen power CB has popped.
The A/C should be on its own circuit as stated above, but anything is possible in an RV! :(