Markus,
If you hit the "Refresh" button in the top from the FB App section, you're account information and subscription status will be re-fetched.
If that still doesn't work, please make sure your subscription ID was entered correctly. Beyond that, I'm not sure what the problem is, but if you're still having problems, we'll gladly help.
Finally, if you really want to uninstall JFBConnect completely, you'd need to uninstall JFBConnect from the Joomla Installation manager. Then, you'd manually need to remove each of the #__jfbconnect_xyz tables from your database. We don't currently remove that information during an uninstallation process as it would remove any connections between your users and their Facebook accounts, which would cause big problems for most of our users.
Hope that helps,
Alex