Yeah, it's one big "server". Not one server unit, in physical space. I mean, there's a ton of actual servers running the one 'server'. Still, it is one big virtual server, like EvE or Guild Wars. This is something future MMOs are looking into. It's very compelling, and the technology is finally here to make it happen. Still, there are rough spots to work out.
Yep. If you have three servers and all three crash, there's a good chance you'll find three bugs and be able to fix all of them in the time it currently takes to fix one bug. Having your Fed character on one server and your Klingon on another would mean you could play during most downtimes. I think one realm is a bad decision, though I obviously don't know all the factors that went into it. (I do like the idea that if you and a friend both play on the same faction, you can play together. I get that advantage.)
This game is not one huge open server .. there is one Hub from which you get shuffled to instanced zones with a max of 5 players in each instance. If you signed up for massive multiplayer you have been cheated like everyone else.