Yes, JFBConnect is a component with multiple plugins as well.
As for JomSocial's Facebook integration, to work properly with JFBConnect, you should disable it by removing the API/Secret keys from their Facebook Connect configuration area.
We have plenty of users who are using JomSocial and JoomlaArt templates, so you shouldn't run into many issues with that combo.. if you do though, just let us know, and we can help!
Thanks,
Alex