1) All three branches have 3-year scholarships. I believe a three year AF scholarship requires 4 year AD payback. In terms of number of 3 year scholarships it would be AF>Army~Navy.
4 years would be Army>Navy>AF.
2) The fiscal year begins Oct. but you should prepare your packet before hand. I recommend getting your paper work, MEPS physical, and everything started early. There are a lot of hiccups that can arise and it requires time to rectify them. Heck, I spent 1 week just trying to find a traffic ticket I received as a HS student.
3) Three year scholarships are generally more competitive because there are far less of them. You're competing against people whom were waitlisted for the 4 year HPSP , currently enrolled dental students (D1), and also students entering UOP.
For the Army, there were about ~25 3 year scholarships.