Auhenticator has an option to generate back up codes. it creates one or two QR codes that you can scan in a new Authenticator app and it will clone all of your accounts.
Not true, I just did it a few weeks ago when moving to a new phone. Just screenshotted the backup QR code and when I got my new phone later I used the screenshot.
All screenshot/print/save functionality is disabled when you have the codes up on your phone.
You need an actual camera on a second device to save them in most cases.