Free advice is worth exactly what you paid for it. But, given that:
1. Yes. The physician category is only for GME training. This is up to the place that is hiring you and they should be able to answer it for you.
2. This is very complicated to answer. First, it depends upon what country you are coming from. You start here to see if your home country is on this list:
Skill List by Country
If it's not on that list, you move on to the funding question below. If it is, then you need to look up the types of research that trigger the 2 year rule, and that's here:
2009 Revised Exchange Visitor Skills List
Medical research is type 51.12. There is also a group 26 for Biological research. If your country is listed here and Group 51 is included, then you will have a 2 year HRR. If not, then...
The last question is whether your research is funded by your home gov't, or the US gov't. If your home gov't is paying for anything, then your get a 2 year HRR. If you're being funded by a specific US funding program for international exchange students, then you get a 2 year HRR. If your PI gets funding from the US gov't via an R01 or similar grant, then you PROBABLY
do not get a 2 year HRR. But here's the fun part: it's completely up to the State Dept when they review your visa app. You won't know until you actually get it -- and once you get it, you can't give it back.
3. Theoretically yes if you don't have a 2 year HRR. EB-1's are not easy to come by. If you have enough scholarly activity to qualify, you could probably just get one now. It's unlikely you'd generate the publications in 1 - 1.5 years needed to qualify for an EB-1, although anything is possible. But you'd need to qualify, apply, and get it in time for the match, or be happy with a clinical J. Timing wise, this is going to be very difficult. Applications (where you'll declare your visa plans) are due on Sept 15th, so you'd have to have a completed EB-1 by then. From my very limited experience, the application process is at least 6 months, so you'd need to qualify and apply by March of the first year of your fellowship -- since you'll have started in July, you'd only have 9 months to get enough done to qualify.
4. Places that don't take IMG's won't care if you were a US citizen and didn't need a visa at all -- they won't take you. It's possible that having an EB-1 with an EAD would put you in the same bin as US-IMG's, as you wouldn't need a visa. It's also possible that programs would be unfamiliar with the EB-1 program and not consider you at all.