JuJ,
Whew.. took a bit, but we think we found the issue with the login link. We need to run this through our automated tests (to make sure it doesn't break non-sh404 or other unforseen problems, so we don't have a release available with the fix. If you want to test though, it's a simple one-line change and that will hopefully get you set up.
In the /components/com_jfbconnect/libraries/facebook.php file, on line 95, you'll see the definition for $loginLink = ... Replace that line with:
$loginLink = $uri->toString(array('scheme', 'host')).JRoute::_("index.php?option=com_jfbconnect&task=loginFacebookUser&return=" . base64_encode($return));
Please let us know if that fixes you up, we'd love to hear confirmation. We'll be releasing 3.2.1 later this week, and this change will be included as well as a few other fixes for minor issues (though this is one of the bigger ones).
Thanks for your patience, and good luck!