For the update issue, I'm assuming you mean from the Joomla Update Manager? If so, try purging the cache. If that doesn't work, please start a new thread and we can look into it more. This thread is pretty lengthy, and that's getting off topic.
Regarding the refresh issue, glad you got it! Caching can be wonderul, but also a pain. Browser caching for HTML output (non-static) should never be browser cached on a site that allows logins.. for reasons you've just seen. Anyways, glad you got it going. If you need anything else, just let us know.. we'll be here.
Finally, if you haven't already, please consider leaving a rating and review on the Joomla Extension Directory for JFBConnect, or our support. It's certainly not required, but very appreciated:
extensions.joomla.org/extensions/social-...ook-integration/7215
Thanks, and good luck!
Alex