Everything is messed up on my phone I'm using the stock system on my Samsung GS3, and one day the phone just started restarting itself randomly. It might restart itself once or twice a day, and no pattern was observed. Then all in a sudden in one of those weird self-restarting the phone resets itself. All app data are gone but system settings left untouched.

Then comes the waves of error of Google stuff. As soon as you unlock the screen, all sort of errors popped up randomly, like "Google Services Framework has stopped", "Google App has stopped", and "The process com.google.process.gapps has stopped", etc. The Gmail app doesn't load, and you can't view the list of installed apps in the Play Store.

When connected to a PC, with adb it says it's connected, and I can access the system through adb, but I can't use Windows' explorer to navigate the storage system.

I didn't flash any custom OS. I do have root and xposed installed but there is no special action I did that causes this to happen. The syncing of the Google apps are also messed up, and it seems only apps related to Google are having errors.

Without manually resetting (for real) the phone, is there any way to fix this? Once in a while the phone is still resetting itself and this is driving me crazy.
First turn airplane mode on that should stop all erros google sync alike.

Then go to settings > account > remove google account.

Then go to where you manage your apps and delete all data + cache of every google app (play store google+ google play services etc).

Also look for an option called something "Redefine preferences" sorry my phone is not on English so may be a little different option but with the same meaning do it then reboot your phone and desative airplane mode see if it's all ok.

If you want you can also do an backup via your PC while on airplane mode so if that steps don't help and you really need to reset you will be OK