Patrick,
During the login process, the user must accept that their profile information will be imported. The request to post to the wall, per Facebook, is an optional permission. It comes up in a 2nd window and can be 'skipped'. When that happens, JFBConnect doesn't post to the wall. When I registered, I skipped that permission.
The automatic login does seem to be working, but right now, there is a bug with Facebook that we're looking into. Basically, if the user is logged into Facebook and has already created an account on your site, but isn't currently logged into your site, it takes 2 pages loads for the user to automatically log in. There are reasons I can gladly go into, but after a refresh, I was logged into your site. It's something we're looking into fixing, but don't have an ETA on the release.
The Fanbox at the bottom of your page seems to be working. The one at the top, I think, doesn't look right because the height is too small. If you want to show the header, stream, and faces, you should use a height closer to 500px, instead of 200px as it's currently set.
I went through a few pages and hit the Like button, and it seemed to work.
If you can explain what's not working with the modules, that will help give a better answer.
Thanks,
Alex