One of the problems here is that, when the ship pops up for the first time, our heroes indicate they do not recognize it - meaning they don't recognize its shape
. That makes it a bit less likely that the design would be in common use, with the Vengeance
reflecting either standard production or a special modification. Or then it makes our bunch of heroes ignorant.
Which is perfectly excusable if they have indeed been out in deep space for a few years. But if that were true, why would a five-year sortie be such a big deal for Kirk? They can't have been gone for as long as it takes to produce a ship like that out in the open (we get an idea of the timescale from the previous movie showing us the NCC-1701 construction timeline in some detail).
Perhaps the heroes aren't ignorant at all, and actually do recognize the shape, and Kirk merely swiftly asks Khan for additional, in-depth information he knows Khan possesses...
Whether Marcus would have control over ship procurement policy, it's difficult to tell; in some militaries of the past, a man like him would have had that exact control, but in modern ones it would be uncommon. But the clearance to launch assassination missions and destroy fellow starships as situation warrants could be well within his grasp, as many modern militaries would provide that sort of leeway in a comparable high-tension situation.