I think it's a lot like the Borg, a single collective mind when they are linked. But unlike the Borg, the members are able to think and behave independently when they are not linked.
I have always wondered what type of facilities they would need to have to do all their evil bidding. If they exist in a big soup pool of people, I guess they don't need houses or roads or real infrastructure the way solids would. But where do they do their genetic engineering to make Vorta and Jem'Hadar? Where do they build ships, develop science, etc. I imagine there has to be more than just that random rock edge on their planet, right?
The female changeling looked to be the leader of the Dominion forces in the Alpha Quadrant, but not necessarily the leader of the entire Dominion. That would be like assuming Eisenhower was the leader of the United States during World War II.
Great analogy, too bad McBain killed it
I never got the impression that she ran the whole Dominion or the Great Link. Actually, I'm betting that no one runs the Great Link. I think they exist the same way the Borg were originally conceived (that is until motion picture dramatic license added an over-sexed Borg Queen)