If you changed domains then you need to edit your Facebook application and correct all of your domains there. Even then Facebook may store what domain was used to initially authorize and reject it. I don't know the backend of how that functions on Facebook. Aside from that the only way CB Connect knows what user the social account belongs to is by their social site ID (e.g. their Facebook ID).

I can't force you to upgrade, but you're going to continue to run into problems using older releases; the purpose of new releases is bug fixes and features all of which you will not have. As for your template issue we now support template overrides in CB 2.0.4 so it's possible to create a CB override template so you'll never lose your changes again.

You can't have 2 users with the same email address. Joomla will not allow it. So that error message is normal behavior. Login via CB login module normally, click Link with Facebook, logout, now click Sign in with Facebook and you should be logged in fine and should be able to continue to login with either CB or Facebook since the two accounts are now linked.

I really don't know what more to advise. If you're not going to upgrade to new releases, which solves some known connectivity issues then you're going to continue to have issues. If your issue persists with the latest release, which I am unable to confirm, then I can investigate further. The latest release is CB Connect 6.0.4, but it requires CB 2.0.4 at minimum.

There were some major endpoint bugs found that are now fixed in 6.0.4. These endpoint bugs cause session data to be mismatched and lost so CB Connect couldn't even see they were connected. It's also not even possible for CB Connect to register a user without a social site id so I'm not sure how that's even happening for you; the entire process is cancelled if it's not present. The only explanation for that happening is something else installed is acting on the after profile update and/or after registration triggers and is clearing the field.