Yes, yes it would. When using JomSocial with JFBConnect, you should disable JomSocial's Facebook Integration altogether. You can easily re-add JFBConnect's Login With Facebook button to replace JomSocial's version, but unfortunately, we can't do this automatically. For more information on how to do that see our guide:
Using JFBConnect's Facebook Integration with JomSocial
As for the Login module missing, that's definitely strange. The picture above actually indicates it's installed but not published, which is normal. It should be in your list somewhere, or, if you want to use it, you may need to hit the "New" button to create a new instance of it. Actually publishing the module isn't required, as you can use the {JFBCLogin} tags, as described in the page linked above.
Hope this helps, but if you have other questions, just let us know!
Alex
JFBConnect Login not published
