Mark,
Questions are always welcome. We have a subscription system for a reason, Facebook (and websites in general) are complex. We have no problem charging for our component and support. Take advantage of it, and thank you for supporting us.
As for your question, to being, I just looked at the admins tag you used, and I think it's incorrect. According to Facebook, this should be the Facebook IDs of the users, not their names:
fb:admins or fb:app_id - A comma-separated list of either Facebook user IDs or a Facebook Platform application ID that administers this page. It is valid to include both fb:admins and fb:app_id on your page
You can get your Facebook ID from Facebook or even in the User Map tab of JFBConnect for the specific users that are connected to your site with Joomla accounts.
As for the Like being for the same page across the site, I'm seeing this too. I believe the problem is that you have a default Open Graph tag of your home page specified. In the Like button, we specify the page a user is liking, but then Facebook scans that page for the Open Graph URL tag to see if there's a better (canonical) link to use.. Since that's set to your home page, I think that's causing all Likes to go there.
Can you remove this from the defaults box in the Open Graph area? Obviously, we should make the repurcussions of that tag more apparent as well.
Hopefully this fixes your right up, but if you have other issues/questions, just let us know!