I'm starting the NIH track through PHS this year and can answer a few of your questions.
The Officer Basic Course (OBC) lasts two weeks and is held at the National Convention Center not far from DC. Its death by powerpoint, lots of information on the history and ethos and internal workings of the PHS, plus some team building exercises. I'm finishing up the first week right now actually. There are 2 of us USUHS students here out of a class of 45, with everyone else coming from a very broad range of health professionals (MD's, dentists, nurses, PA's, pharmacists, researchers, etc) working for a wide variety of federal agencies like the CDC, NIH, Bureau of Prisons, IHS, FDA. Its very laid back, even compared to the officer trainings that other USUHS students do, from what I understand.
There are physical fitness requirements for the PHS. 1.5-mile run, push-ups and sit-ups. You can find more information here:
http://usphs-hso.org/pac/subcommittees/readiness/readiness_information.shtml#physical
PHS officers do sometimes deploy and serve in positions overseas. The US is certainly their main focus, but if international work is a priority of yours then you can most likely make it abroad at some point in your career. One of our OBC instructors spent a year in Brazil as a Health Liaison with the embassy, for example, and my PHS contact officer at NIH does a significant amount of traveling on research related trips. PHS officers will deploy to international disasters as well. I know they sent people to the 2004 tsunami, for example, and to several Central American earthquakes.
You can spend your entire career in one position or location, if you like. Most people move around for career advancement purposes though, or just to try something new. For example, once I'm done with my payback commitment at NIH, I can apply for any MD or admin job that I'm qualified for at the CDC, FDA, IHS or any other organization that the PHS has a relationship with. Or I could stay at NIH. There are quite a few options. Here's a link to the agencies/organizations that PHS works with:
http://www.usphs.gov/AboutUs/agencies.aspx
PHS officers deploy for a maximum of two weeks a year to respond to things like hurricanes, earthquakes, epidemics, and other disasters. They'll also deploy to provide public health expertise during scheduled large public events sometimes. One PHS officer I met deployed to Obama's inauguration in DC, for example, just to be on hand in case something went wrong. Its nothing like deploying with the military. You'll return to your usual job after a week or two.
My stats (FYI):
3.51 gpa
3.56 sgpa
36 MCAT (12 12 12)
I wasn't premed my first few years of undergrad and thought B's were perfectly fine so my gpa is a little low. I had a strong upward trend though. Finished out my last 3 semesters with 3.9/4.0's.
Your resume has alot to do with being eligible for the NIH slots. Its the National Institute of Allergy and Infections Disease (NIAID) that's actually paying for the slots, and they're the institute you'll work for when you're done with your training, so they're interested in people with research and lab experience that are committed to a career in infectious disease. I've done some ID-related research (1st author publication in a small but still peer-reviewed journal and a poster presentation at an international ID conference) and about 2 years of normal undergrad bench research with 1 poster coming from it. Worked as a microbiologist for a year after undergrad, which helped as well, I think.
I don't know how competitive the spots are, but I think it probably varies a bit year to year. Its a tall order deciding your subspecialty before even beginning med school. Kind of like choosing an undergraduate major while you're in middle school. Definitely not for everyone. Plus its not a very well known option at all (I didn't even find out about it until my interview day at USUHS), so I think the pool of people who apply is probably pretty small. My recommendation would be that if you're at all interested in a career in ID you should apply and see how it goes so you at least have the option available if you get accepted.
The Indian Health Service spots at USUHS are probably similar in that they're a great fit for specific types of people but definitely not for everyone. If you want to practice primary care in a resource-poor, undeserved setting (which would be very fulfilling work IMO) then IHS is a great way to go. But again you have to decide before even starting medical school, so its a leap of faith.
OK I think that more or less answers your questions. I'll be happy to help with any others you have.