You can use full paths at the end of the App URL, like:
apps.facebook.com/joomla-extensions/forums
apps.facebook.com/joomla-extensions/blog
However, the URL won't visibly change after the initial landing page since the content is shown within an iFrame. That should let you create many different app landing pages for your site though, if that's what you're looking for.
I'm not sure about GET variables in particular and how they would work, but I think that's possible as well.. just haven't really tested with them.
Finally, we don't have any specific integration with Zoo. JFBConnect is compatible with just about every extension out there, so users that login through Facebook are seen just like any other Joomla user. You can also add our {JFBCLike} or {JFBCComments} (or other) tags to your Zoo articles or template to have the FB widgets appear. The notification email on new FB Likes and Comments and comments will work within Zoo, etc, etc. So, you shouldn't have problems using JFBConnect with Zoo, but if you have more specific requests, let me know.
Thanks,
Alex