Will these bolt straight to my factory fog light locations?

Yes. These mount at OEM points with no drilling or bracket modification needed. Test-fit before final wiring to confirm alignment.

Do I need to wire these to a switch, or do they run off the factory fog light circuit?

These housings are plug-and-play for the factory fog circuit if your harness is already in place. If your car doesn't have fog lights wired from the factory, you'll need to run power and ground separately or add an aftermarket switch.

Can I replace just one fog light, or do I have to buy the pair?

This is a pair — both driver and passenger sides. If you only need one, you'll have a spare, but individual housings aren't sold separately here.