The auto-login issue is something that may be a problem introduced by Facebook with a recent change they made to how they save the cookie. We're looking into a solution, but for now, the auto-login on most sites will only happen after the 2nd page navigated too. If logged in, on the first page, Facebook will store the cookie. On the 2nd page, JFBConnect will detect this and log them in.
For the redirects that take place after a user logs in, you can find these in the /components/com_jfbconnect/controllers/loginregister.php file. There's a "login()" function which all methods of logging in user (manual, auto, registration). At the bottom of this function, you can see all the different types of logging in that we handle, depending on where they are coming from and your configuration settings. Hopefully, you can get your code in there, but if you need help, just let us know.
Thanks,
Alex