Weird problems after recovery from security breach

Had you just overwrote site from backup? Not a good way since it may easily leave broken files or even backdoors.

It is best to erase site completely, then copy clean WordPress archive and copy of your files from backup there. If possible it’s best to restore database from pre-hack backup as well.

If these are not possible I suggest you find someone who handles such cases professionally. There is now way to comprehensively advice on hacking case “in theory”.