What’s the name for this very thin metal sanding disk for use in a drill

I've had pretty good luck with Ryobi tools in the past, and the drill you are looking at will certainly do what you want it to.

Normally I'd recommend a cordless drill to just about anybody, but if you find that you will hardly ever use it, a corded drill might be better. No point in having a cordless drill if the battery is always dead when you need it because it sat around for 6 months without being used or charged.

Have you tried using a Screw Extractor bit?

They are made for this purpose. You basically put it into your drill and when the drill slowly turns in reverse, the bit bites into the screw and tries to unscrew it simultaneously.