For the first issue, it sounds like the user is still logged into Facebook. So, when the normal login popup appears, the account that's logged into Facebook is being logged into your site. You may want to disable the "Log users out of Joomla only" setting so that when they log out of your site, they log out of Facebook as well. That way, when they use the Login With Facebook button, they'll need to login to Facebook first.
For the second issue, you look to still have JomSocial's Facebook integration enabled. Both JFBConnect and JomSocial's FB integration can't be enabled at the same time. Please read over the following information for integrating with JomSocial:
www.sourcecoast.com/jfbconnect/docs/thir...ration-for-jomsocial
Hope that helps!
Alex