Everything is messed up on my phone
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