IPad – Is FaceTime available on iPad

The short answer - you can either call a phone number (iPhone + FaceTime) or an AppleID (iPod/Mac/iPad + FaceTime) and you can't call another device with the same number.

To call back to your mac (or any other AppleID device) - you'll have to make a second account with a different Apple ID. Similarly - there's no easy way to get the phone number into another device since that gets authenticated over SMS in the background and not user/password for AppleID.

If you are calling from an iPhone - you can call your AppleID devices (they all ring and any one can pick up), but for AppleID based calls - you need to call a different AppleID unless Apple ever changes the current software.

Last clarification - AppleID is just a string but most people use an email address since that is more likely to be unique to one person.

It's a bit of a drastic move, but why not delete the preference files for FaceTime? This should put FaceTime in an uninitialized state (at least for preferences, perhaps not for configured accounts).

Close FaceTime, click on the Finder, then hit the Go menu and choose Go to Folder….

Enter ~/Library/Preferences into the box and press enter. Look for any files that start with "com.apple.facetime" and move them to another folder (for backup purposes).

Open FaceTime back up, check your preferences, and see if the Auto-Accept continues to occur.