The profile import is the largest integration between JFBConnect and CB. With it, you can select exactly what fields from Facebook are imported and what fields within CB they go into, so you have full control over the information pulled in.
Beyond that:
* Facebook has it's own Request/invitation system that we support, and it's not related to CB.
* During registration and/or Login, you can configure JFBConnect to import the users last FB status message into their CB wall
I'm not sure what you mean by 'every event related to groups'. We don't have any integration between events and groups, but if there's something you're looking for, we'd love to hear it. With JomSocial, for instance, we do have Open Graph Action integration for Groups. So, when a user joins a group on JomSocial, a Timeline event can be automatically posted to their wall without any popups or confirmations. It's great for promotion, and we're expanding the Open Graph Action integration into other areas, so your feedback would be great.
Hope that helps explain,
Alex