Okay, so the problem seems to be that I actually can't sync firefox and maybe the passwords were saved only in the cloud. Could that be? I just hope I remember my Firefoy Sync password soon...

Unfortunately, I seem not to remember my sync password. But shouldn't it be saved in the backup profile folder "Refresh Firefox" created?

Your passwords should have survived the Refresh process. But that "Old Firefox Data" does indicate that a Refresh was done. Any chance that you tired of waiting the the Refresh process to be completed and closed Firefox before that process was completed? From my experience with Refresh, it took over 5 minutes to finish the process. In any case if Firefox was closed while the Refresh process was running, your data is gone; it was running in RAM and was deleted when Firefox was closed.

But "start fresh" almost sounds like the feature where a new Profile would be offered when the Developer Edition is installed; although I'm not 100% sure of that. It has been a few years since I last used the Web Developer / Aurora version.

Load about:profiles in the Location Bar and see how many Profiles that you have. Your passwords may be in a different Profile.

If you forgot your Sync / Firefox Account password don't reset your password, that triggers clearing of your user data on the Sync server as a new password makes your data useless. The original password was used to create the encryption algorithm so the new password would be unable to decrypt the data.

The about:profiles hint was great! What actually happened is that not only did the Developer Edition refresh but also set the new profile as the default for all other browsers. However, the backup it created was only for the Developer profile that has been used before. So all I needed to do was switch back to the correct profile.

It is a bit strange this happened. Maybe there was a change in that before these browsers used different profiles but now they only one?

In the event that the passwords information is lost, you should record all information in a separate text file somewhere else on your hard drive, or written down. You can easily copy and paste if you need to do so. If you are concerned about someone else looking at that file, you can compress it using a password.

The Developer Edition would normally use its own exclusive profile unless you would have changed that in the startup settings and have a ignore-dev-edition-profile file in the Firefox folder where profiles.ini is located present (not sure it has the same name on Windows).

• Options/Preferences -> General: Startup
  Allow Firefox Developer Edition and Firefox to run at the same time