People handle drill and med school fine. It's do-able, it's just a lot easier as a medical student rather than MOS qualified student.
What are you talking about when you say the "AMEDD program?" I'm not sure what you mean. You can join as a medical student and just drill or you can take funds as a medical student that require obligated payback by drilling throughout and after residency (google MDSSP).
But both require you to be an officer and therefore both will require you to be a U.S. citizen. So you can either try to get out of your enlistment (which you need to do before shipping off to basic) or serve it out and try to switch to direct commission to a med student MOS after you have your citizenship in hand. I don't know folks who have gone the latter route and can't give you advice on that.
Depends on where you go to school for sure. I went to a school that was small and community based ( no residents or academic institution ) which means you will get to do EVERYTHING but you won't ha have free time either, including having a drill weekend available.