Unfortunately, no quick and easy answers, especially with a multi-site configuration (which we have not tested).
Couple things to check first.
- Is the user being created properly in the Joomla database?
- Is there a corresponding row in the JFBConnect Usermap table (accessible in the JFBConnect admin component).
Next, move onto the Facebook configuration. If you use JFBConnect on one site (not across multiple domains, and preferrably the 'root' site, if possible), does it work there? Facebook is finnicky with it's url's that you setup in the developer area. Please make sure these are correct, and that the Base Domain (allowing operation across multiple sub-domains) is correct.
As for the username/email setting, I'd like to get some answers to the above first, and we can go from there. Another option you may want to try is setting the "Create New Users" setting to "No". That's what we use on this site as it's does a silent registration and automatically creates a Joomla user with the username "fb_xxxxxx". On a return visit, they can't log in through Joomla, only through Facebook, but in every other way are a unique Joomla user (to other components and the system as a whole). The newest version of JFBConnect (v2.6, just relesed about.. oh 20 minutes ago), grabs the user's correct Facebook email address and creates a Joomla user with it.
P.S. I just added JFBConnect to your subscription on this site, as I saw you purchased it on CMS Market at the end of last month. We just transferred that here, so you know.