Cat,
Sorry for the delay. I'm testing things right now, and just want to assure you that we'll gladly extend the refund policy for a little bit past the 30-day period. If we can't find a resolution to your problem, or you're unsatisfied until the 20th of May, feel free to take advantage of our guarantee. Beyond that time period, it becomes harder for us to process refunds through some of our merchant accounts, but that will hopefully be enough time to get you settled and satisfied.
Now, on to your issue

1) First thing I notice is that you're using JomSocial 2.2RC1. I don't know if this is the cause of some issues, but would highly suggest updating to 2.2.2, which I believe is the most current release.
2) In JomSocial, your Facebook API and Secret key were set. I removed these as there can only be 1 Facebook Connect extension in control on your site.
3) I deleted my account that I created a week or so back, and just re-registered. Upon registration, the New User redirection, which is set to a menu item of "URL" type gave me a 404 error. I'm not sure if this is a JFBConnect issue not handling URL type menus or if it's something with the old version of JomSocial you're using. We can test the URL portion, but again, please consider updating
4) My profile was imported as expected. I can see it in the admin area and on the front-end when I hit "Edit Profile".
5) Finally, regarding the logging out, if you're using a logout button that is not part of the JFBConnect module, this will happen. Our logout button has extra functionality to log the user out of Facebook as well (so they aren't automatically logged back in). Other logout buttons don't do this, which means that the user will be automatically logged back in. We're looking into ways to attach our logout of Facebook functionality to any logout button automatically. However, until that's done, you'd need to add a snippet of code to logout buttons, which we can show you how to do if you know the logout button you want to add this code too.
Whew. Again, sorry for the delay, hope this helps, and let us know how we can help further. We'll be more responsive going forward. Facebook made a minor change over the weekend that threw us for an investigation loop, which slowed down our response time a bit.
Thanks,
Alex