Well, I do speak Dutch and German and the two words in German are certainly related. In fact, in my Dutch/German dictionary, gesellig is translated as gezellig (not the first definition though) and gemütlich is translated as gezllig. So, if A=C and B=C, then A=B (OK, these are words, not numbers, but I'm showing a relationship).

If you think you can be gemütlich (or gezellig) by yourself, that's a context that is new to me.

I can certainly understand your point about Oktoberfest and gemütlich (although I've never been there myself), as I can't see how you could call a tent with several hundred people "cozy." However, the social aspect of the word could apply provided you've "connected" with some of those people. Nevertheless, I would agree that a mass event could probably never be called gemütlich or gezellig.