Captain Pike informs civilian Kirk (after the barfight with the Starfleeters) that he could graduate the academy in four years...and have his own ship in EIGHT!
This statement is problematic, since we can't tell what the "eight years" means. Is it eight years from that moment, aka four years out of the Academy, or eight years after graduating. I guess the former is implied. Either way, I think Pike means Kirk could do it. Obviously, getting one's own ship within a decade of finishing training would be unusual in peacetime, but Pike seems to think Kirk has something special. However, I doubt Pike imagined Kirk would come right out of the Academy and become his successor aboard the Enterprise.
Unless I'm mistaken, Admiral Tyler Perry graduates Kirk as a CAPTAIN...not an ensign or whatever Starfleet Academy calls their O-1s
I believe the rank most Starfleet officers get coming out of the Academy is Ensign. Also, I am certain that Kirk becoming a Captain is very unusual, and a reward for his actions. Considering everything he did in this movie, I think the promotion and command of the Enterprise is somewhat justified. he'd proved he could command her crew, and someone had to replace Pike.
BTW, when I first saw stills of "Leonard H. "Bones" McCoy, I thought cool, they found a Gary Lockwood lookalike to play Kirk's best friend in the academy, Gary Mitchell.
No Gary here, folks.
Since they didn't spend a lot of time on Kirk at the Academy (he joined, then they skipped ahead 3 years), it's understandable that they didn't reference every relationship he ever formed there. Also, I seem to recall that Mitchell was a student of Kirk's when he was a teacher at the Academy, not his contemporary. Obviously, this hasn't happened yet, and may well not take place anyway.