I imagine I'm not the only one that genuinely enjoys Frameworks community/social networking feature/forum. More so than most any other legitimate social network. I really enjoy the work, ideas, and complexities that go into it. One really great idea in my opinion is the badge system.
In answer to your last question, here’s a complete list of badges. In answer to your first three, I believe all badge awarding is public. Looks like there are a couple that have never been awarded before, so that’s a solid bet for most rare badge there is