The episode plays out nicely prima facie, but the truth about Khan could easily be more complex. On awakening, his first and only question is "How long?". In which circumstances would this really be relevant? A journey intended to achieve a destination would rather call for the question "Where?", not "When?"...
I disagree completely. He probably knows something has gone wrong since humans have awoken him. For all we know, he might also be able to feel that he has been "sleeping" for much longer than intended. Whether he asks "when" or "where" doesn't make him more or less realistic. When I've been sleeping for too long the first thing I do is look at the clock.
If I for some reason don't remember where I went to sleep, of course I wonder where I am when I wake up. If I am traveling on a boat and have slept I wonder both what time it is AND where I am. I most often ask what time it is because I know what time I will arrive at my destination.
Anyway, I would probably ask "how long" if I had been on a spaceship and feeling as if I was halfdead and the people bending over me had thingamajigs looking a lot more advanced than what I was used to.