The guide wrote by nemesis_fs works for me. Thanks a lot!
Now I can play the game again, but this is really stupid nonetheless. Bohemia screwed up something with their updates and hotfixes, because I haven't touched anything in my drivers in MONTHS, and that was before these problems appeared.

Anyway, I'm glad the problem is solved now, thanks to all you guys who helped me.

Doesn't work. I changed drivers and both those problems remain.

I don't think that applies to me, because the Catalyst Control Center has a completely different look for me. That's the old version. There's no troubleshooting tab in my Catalyst Center or Display adapter, so I can't change that value.
Also I have the Catalyst Omega drivers, so I don't think they're outdated at all.

No, I'm not. All Catalyst settings - AA settings included - are in the "Use application settings" mode.