The Marine Corps falls under the Department of the Navy, but are generally considered separate entities; i.e. never call a Marine a sailor (or a soldier for that matter).
Yes, capitalize service academies. Acronyms are generally acceptable albeit less formal, as are their more common names (USNA = Annapolis, USMA = West Point, USMMA = Kings' Point, etc).
To the best of my knowledge, that is. Hope I helped.