Hello Pyro
You won't be able to copy user passwords, user preferences, etc. If you were able to export that, anyone could. You would need that to be provided by the system admin of the old server (in this case by Editthis), and at that point, you are better off getting a db dump.
Skins and special pages are either provided by the core MediaWiki or by an extension. Editthis uses very little extensions
https://editthis.info/wiki/Special:Version albeit ControlPanel may be a custom one (I can't find that extension). If you have access to edit LocalSettings.php itself at the new host, it should be an appropriate replacement.