So I installed a custom ROM (Paranoid Android) and now apps like Facebook aren't compatible.
That is quite strange. After flashing the rom, did you flash a compatible gapps zip as well? If so, after the device booted, did you alter the build.prop at all?
I just installed the new PA from yesterday. After that I just continued with the normal set-up.
Have you played around with the Hybrid Engine (specifically the modes such as Phone, Phablet and tablet) as I seem to recall this affecting some people. Check the properties of the Playstore in Hybrid engine as it could be that the Play Store thinks your phone is a tablet (why that would a 'universal' app like FB I have no idea though)
What version did you flash? One of the early Halo alpha versions had this issue. I would flash either the latest alpha, or the latest stable release.
I just flashed stock, I'm flashing a stable version of Paranoid Android now.
Separate names with a comma.