Shortest stay I would even consider is a year, everyone who leaves in 6 months either 1. Had just gotten used to things and regrets leaving after such a short time. 2. Wasn't ready for Japan and couldn't handle any more thus, quickly went back home.
Medical huh? Let's see. It depends on when you want to study. There are rotary scholarships you might be able to check into, and then of course there is the study abroad department at the college you would attend (this is by far the best source of information you'd have close to you I'm sure). It depends what you want to do, and why. If you just say "I want to study abroad" without giving a reason how it will help, or how you can give to others, don't count on going though.