Do I need fasteners to install this bracket?

Mounting hardware is not confirmed in this listing. You'll want to test-fit the bracket against your bumper cover before committing to fasteners or adhesive—different trim levels may have slight variations in mounting geometry.

Can I install just the right bracket, or do I need both sides?

The right bracket handles its side of the bumper cover. If your left bracket is still solid, you can run right-only. If you're replacing both covers or the left side is damaged, grab the left bracket too to keep things symmetrical and stable.

Should I prep or paint this before installation?

The bracket ships ready to install. If you want it to match your bumper cover finish, light sanding and a quick coat of primer + paint will blend it in—just don't let paint pooling interfere with the mounting surfaces.