1) There could be a few issues here. First, make sure you don't have the System - Cache plugin enabled. That plugin generally shouldn't be enabled on sites that allow user authentication.
Next, it looks like you're using a 3rd party SEF extension. If so, please make sure it is set to 'skip' altering JFBConnect URLs. That could be causing some problems, though I don't think this is it. However, when I'm in JomSocial and I click the 'circle with a vertical line through it' logout button, I'm brought to the following page, which causes a redirect loop:
http://fijitravel.directory/en/component/users/?task=user.logout&caa18007d37fe5d1b4a79d92d4926b02=1&return=L2VuL2hhbmdvdXQuaHRtbA==&Itemid=1
Since that has a redirect loop, it could mean other URLs are having issues as well.
2) I can't speak to their support, but I'll tell you that our forums are open for all to see whether you have a subscription or not. So is our documentation. It's just how we operate as we think it's the best way to win over customers
As to your problem here, I've never heard of this issue. Can you try disabling the JFBConnect Authentication, System and User plugins and see if the problem persists? Disabling all of those will completely shut JFBConnect off from functioning on your site. If the problem remains, it indicates that JFBConnect isn't the cause. If the problem goes away, let us know and we'll do what we can to investigate more.
Thanks,
Alex