Alec,
The login/register process can be done using the Authenticate Referrals feature of Facebook Apps. That works if you're app is being viewed in an App Canvas or Page Tab area (ie, within Facebook.com). You can't auto-register or force users to register to your standalone site.
As for logging out automatically, we don't currently offer that if they log out of Facebook, but there are likely some pretty easy ways we could help you implement that. It's simply not something we've ever had requested, so it's not a feature yet.
Hope that helps,
Alex
JFBConnect facebook app integration
