Try logging into this site, or our
Demo Site
and see if the login time is substantially different. In general, it should only take a few seconds for the authentication to occur, but there's always some variability in that since you're connecting to a 3rd party. Additionally, any system, user, and authentication plugins along with even browser add-ons can all affect the process. When I tested logging in on your site, I didn't see anything out of the ordinary.
As for the JomSocial Activity status, simply go to the Profiles configuration area of JFBConnect and disable the "Import Status" setting.
Alex