1) For the automatic inclusion of the Comment box (that you configure in the Social tab), you'll need to enable the JFBCContent plugin for those boxes to automatically appear. I realize now that we don't make that very clear.
You won't want to use the JFBCComment module for this. That's good when you want a comment box on a specific page, or specific non-Joomla Core Content section.
2) The comments will only post a user's profile when they comment on something. We're investigating ways to let comments appear automatically in other areas, but Facebook has limitations on what can be automated. You can setup the JFBCFan module to show your Website Like page and people can Like it from the widget on your site, but that's all that's available right now.
Hope this helps, and if you have any other questions, just let us know!