Waqas,
Please check the following:
* Make sure that you haven't enabled any JFBCProfile plugins for any extensions you don't also have installed (Don't enable the JomSocial profile integration plugin if you don't have JomSocial, etc)
* If you're using an SEF extension, go into the settings and set it to 'skip' JFBConnect URLs (this doesn't seem to be the case on your site though)
* Go into Global Configuration and disable GZip compression and set Error Reporting to Maximum. The 500 error page may give more details about what the issue is. If so, please post the error here, and we can investigate further.
Hope that helps, but if not, let us know.
Thanks,
Alex