Something is going on with your database, or possibly JomSocial, it seems. There are 'sessions' stored for each visitor. These sessions store the state of user (logged in, user parameters, access tokens to validate forms, etc). On the /network.html page of your site, the Login forms don't work at all. They always return "Invalid Token", which means the token for that user is incorrect. I'm not sure if the problem is specific to that page, JomSocial, or even JFBConnect, but it doesn't look to be caused by JFBConnect.. our extension is just affected by it.
For both issues, can you:
* Try changing the login redirection to a new page, like the Home page, and see if the issue still comes up
* Turn off any caching you may have enabled
* Try turning off SEF URLs and see if that fixes the problem
Let us know if that helps, we'll gladly do what we can, but not sure this is something on our end that we can fix.
Thanks,
Alex