Don't worry about over-stressing the Mac. It's old, and it's probably been unused for a long time, so it wouldn't be a surprise if another capacitor gave out, but using it won't shorten its life noticeably more than leaving it turned off. It's not useful for current work, so you won't be running it 24/7 anyway. My much-abused and hot-rodded original Mac is still in use a couple of hours a week and hasn't worn out yet, though it's needed that yoke connector and the flyback transformer and C1 resoldered where heat cycling cracked the original solder. A cooling fan like a Fanny Mac or a System Saver is a good idea.

As for the Apple II mouse, if the plug on the mouse fits the mouse jack on the back of the Mac, it's OK. They were identical except for color, and the Apple II versions were several colors, not all the "one official color scheme" listed on a certain well-known Apple website. You can't believe everything you read on the internet. Your Mac is exactly what you thought it was in your first post. Good price, and a good save of a classic Mac!