Apps Disappearing from Home Screen and App Manager
I can't tell why your apps disappeared, but I think you're not able to reinstall them because of leftover data files. I used SD Maid to delete data corpses, in order to be able to reinstall some apps after flashing a rom.
Once installed, go to CorpseFinder, scan and then delete the corpses you find. You should then be able to reinstall your missing apps.