The page you linked to is Joomla's registration page. If you're having issues with that page, that's not caused by JFBConnect as we don't modify that page. I'm not sure what would be preventing registration there.
I did just tried to register/login using Facebook, and I got the "500 - JHtml: :bootstrap not supported. File not found." message. So, for me at least, that error isn't gone. Have you tried switching templates, temporarily, to see if that issue goes away? Again, JFBConnect does not implement Bootstrap at all, and that JHTML call, from what I know, should only be used on Joomla 3.0+ sites.
Hope that helps,
Alex