Lessdazed gave what seems to me to be a good answer to most of these questions so I'll just address the remaining one (which unfortunately is one of the one's I don't know as much about.)
In particular, in many countries there is the institution of "Chief Rabbi" that enjoys some government recognition, but which Jewish groups stand behind those?
The Chief Rabbi as a separate institution evolved when in the late Middle Ages the various European states wanted official representatives of the Jewish population to talk to the government. Since for many purposes Jews were often autonomous groups this was the primary method of interaction. Somewhat similarly, in some places such as England, all recognized religions had to have a recognized chief clergy member who was actually considered to serve the monarch. For essentially historical reasons, this job has been generally taken up by a prominent Orthodox Rabbi in most countries where the title exists. In some countries with small Jewish populations (such as Norway and New Zealand) there's very rarely more than one Orthodox Rabbi and so this individual becomes the Chief Rabbi more or less by default. In countries with larger Jewish communities this position can be surrounded by heavy politics and other considerations. Also in some countries the Chief Rabbi is not actually a government recognized position but is the term used to refer to a certain position overseeing some large organization of shulls.
Thanks for all the info. For whatever reason, even though I usually have no problem finding and sorting out information about complicated and controversial topics, I find this one (i.e. the general topic of Jewish religious and ethnic divisions) very difficult to systematize, and your comments have clarified a lot. Of course, even I was much more knowledgeable about the topic, I'd still consider it a valuable opportunity to hear the perspective of someone who has some insider knowledge but nevertheless strives for objectivity.
I was browsing my RSS feed, as one does, and came across a New York Times article, "A Village With the Numbers, Not the Image, of the Poorest Place", about the Satmar Hasidic Jews of Kiryas Joel (NY).
Their interest lies in their extraordinarily high birthrate & population growth, and their poverty - which are connected. From the article:
From Wikipedia:
Robin Hanson has argued that uploaded/emulated minds will establish a new Malthusian/Darwinian equilibrium in "IF UPLOADS COME FIRST: The crack of a future dawn" - an equilibrium in comparison to which our own economy will look like a delusive dreamtime of impossibly unfit and libertine behavior. The demographic transition will not last forever. But despite our own distaste for countless lives living at near-subsistence rather than our own extreme per-capita wealth (see the Repugnant Conclusion), those many lives will be happy ones (even amidst disaster).
So. Are the inhabitants of Kiryas Joel unhappy?