After finally getting access to the wifi button in safe mode, I knew the issue was caused by an app. The only one I had recently installed was TMobile. Sure enough, uninstalling it solved all 3 of these issues.
Well, that was just too easy. Wilfi returned to being unavailable later that night, even in safe mode. Don't know if an app is responsible for this. I'll wait and see if 5.1 corrects the grayed-out wifi before replacing the phone. At least the constant rebooting and icon issues are gone. Until I get updated, I'll look into Reverse Tethering my laptop to avoid being throttled on mobile data.