Star Trek

It wasn't discussed in the show, but Memory Alpha says:

Rick Sternbach notes that the "Prometheus would come in at roughly 1,360 feet (414 meters) in length". (Star Trek: The Magazine Volume 3, Issue 11)

At about twice the size of Voyager, I'd say about twice the crew of an Intrepid Class ship, Voyager last carried 152 people, so the Prometheus should hold about 300 or more. Considering it has three sections, there are likely 100 crewmen in each section plus bridge crew, I imagine they have to have three seperate bridge crews as well, but rougly a crew of 300.

That feels about right.  Personally, I'd keep the crew in the 150 member range.  A ship like that probably has a lot more automation than an average Federation starship.

It is so automated the EMH can operate it, which is, esentially, the ship flying itself, however, given it's size, it probably still needs a lot of people to maintain it, and again, likely needs three bridge crews for the three sections of the ship, not to mention it likely contains a large number of Tactical/assault teams, being an experimental warship.

Would they need three bridge crews or could the segments be flown by remote--similar to modern day combat drones.

I know they can be piloted by remote, but I'm sure a humanoid pilot has much better reaction time and intuition in a combat situation, so I'm guessing they would have three seperate bridge crews, or at least a pilot and gunner/Tactical officer on the other two bridges when fully manned.

Well the Federation was still using manned fighters at the time of the Dominion War, so I guess that could show they don't trust automated combat completely.  Still the Prometheus handled itself pretty well under the remote command of two EMHs--even if it was very vague directions.  A tactical-crew located on the command-section controlling a holographic crew on the other combat sections might do as well or better.

The biggest weak point I see in the Prometheus is the duing the seperation and reassembly operations.  A smart enemy would just start raining weapons fire down as the ship was in a  inbetween state.  Shields and structural integrety fields would most like stretched to limit handling the stress, a heavy weapons barrage might punch through. 

Which is another question: What happens if one segement of the ship is destroyed? can it function to make it back to a base without all the segements?  

Possibly if the two remaining sections linked side by side (think Galaga), otherwise I'd say no, it probably can't

I looked up the blueprints in an old star trek magazine, the modules stack one on top of the other, so perhaps it is possible to rejoin even if one section is destroyed, but I am not sure.