Hello sorry to hear that all your stuff got hacked. In terms of your authenticator problem, Try this:
When you enter the code, log out normally once and then log back in. That way it won't ask for another code when you hop worlds.
Always capitalize your username the same way when you log in. If you type it differently, it will always ask for a code.
Make sure all your passwords for runescape and all your social media are unique. This will prevent these mass hacks.