I have no idea how to solve your issue. If your terms are in database and are correctly displayed on frontend, then it means that either WordPress is corrupted or a plugin/theme is badly interacting with your admin. Of course if Polylang is de-activated, then Polylang does nothing...
I would try de-activating all plugins and switch to a default theme. Then if the problem persists I would try re-installing WordPress files via FTP.