I just visited your website and did not encounter the error you mentioned in your first post. When I attempted to log in via Facebook credentials, I did see an error 0 that something went wrong. Please set Error Reporting to Development mode in Joomla Global Configuration and enable debugging mode in JFBConnect. Without a more detailed error, we would not be able to see what's going wrong.
Also, please verify that the JFBConnect system (jfbcsystem), authentication (jfbconnectauth) and user (jfbconnectuser) plugins are enabled.
-Melissa