Charge the magic mouse with iPad adapter?

The same. I've used to charging my peripherals with bunch of left over. Include 12w with plug head switchable at my place for years no problem. After recently discover one of my Magic Mouse 2 starting to drain battery like bear swimmer. Even I found some users had same issues with recent macOS updates tho.

Yes, you can use the 12 watt adapter. The devices won't use more power than they can handle.