1) would I be subject to GMO if I'm already done with residency at time of entry?
Technically no, actually maybe. The term 'GMO' is generally only used to refer to a billet that would typically be filled by a physician who has completed only an Internship, rather than a full residency, so in that sense, no you would not be required to do a GMO. Actually there are many 'operational' billets in all services that have little to nothing to do with the residency training you have recieved and therefore are, for all intents and purposes, a GMO tour.
FWIW if you don't want to do a GMO tour, I recommend the Navy. Since the have the most opperational billets filled by people who haven't finished a residency (more than half of navy Interns do a GMO before completing residency) they have the fewest opperational billets left for the residency trained. In the army the reverse is true.
2) what would be the minimum active duty required? I saw on Navy website that 3 yrs is minimum.
For you that is probably correct. Occasionally they will allow particularly in demand subspecialists to sign up for a shorter obligation. Right now the wars are winding down, and I don't think they ever extended the option to internists in any event.
3) would I be guaranteed that I could do things aside from working at a VA or US hospital?
In the military there are no guarentees. In the Navy an Internist might work either the floors or general clinic at a major medical center, they might get placed in a teaching role at one of the various family practice hospitals, you might work as an Internist in Guam, or Okinawa, or Japan, or Italy, or they might end up the senior medical officer on an aircraft carrier. You could even draw the short straw and end up at 29 palms (an awful base in the middle surrounded by 2 hours of desert on either side), Guantonamo bay (a prison for all involved), in a 100% admin role as a batallion surgeon (no patients at all), or even supporting Operation deep freeze (the antarctic mission is supported by one military physician). And of course, whatever you do, it can be inturrpted by deployments to our current warzone to support the current war. Your preferences will of course be taken into consideration, but that only really helps if your preferences are different from eveyrone elses preferences.
BTW the guys in the VA are not military physicians. You will not work in one.
4) what kinds of options are there with the reserves, and do they get a chance to travel, etc?
Don't know
5) do I have to do any military residency training?
Everybody does 4-6 weeks of 'basic training'. You can't fail, they don't expect much from you, and you don't learn to shoot. Think summer camp but with more yelling.
6) what about entering after a fellowship such as critical care, would that change anything?
If would change three things:
1) Where you can work. Only big hospitals have critical care units, so you would only work in big hospitals.
2) How often you deploy: ICU guys get sent to war a lot.
3) How much money you lose by doing the military. The salary for critical care in the military is very similar to a general internist, while the civilian salary is obviously much higher for a fellowship trained critical care specialist.