I'm not sure about why there are duplicate fields, but will definitely investigate. As for the no password, that may be a JomSocial bug. We'll test on our page, but having no password is a valid way to create a user in Joomla, and if JomSocial isn't handling that properly... it would affect other things that just Joomla.
As an example, Joomla ships with a GMail authentication and OpenID plugin. Both of these authenticate you against remote servers (similar to what JFBConnect is doing), but in no way can you change your password on those servers from within Joomla. We'll test and see if those authentication plugins work properly with JomSocial, if not though, the best we can do is ask the JomSocial team for their feedback.