I would like to hang something on the firewall in the garage that requires two screws. Is that OK without compromising the firewall?

Lots of stuff hanging from my garage walls.
Typically walls garage wall are fire resistant (have 2 hour fire rating), just 5/8 drywall. Screws in drywall would have not effect on rating.

Screw away.

You can put things ON X rated drywall. According to fire codes you cannot put openings IN them. Try to put the screws into wall studs. We have a rental house and to show you how things were done, this was built in 1974, they have 1/4" ply on the garage side, 5/8 X rated on the inside and a hollow luan door! Our new house has 5/8", a rated door and no wall openings.