Re: The prefix number
Which might just mean that junior officers aren't aware of all the security measures available on a starship. Somebody had to be the cabbage head, and Saavik was the only one who could play that part for the audience.
Which only proves my point. If a Starfleet cadet or junior officer doesn't know of the prefix code's existence, why would a criminal from the twentieth century? That Spock assumed Khan could not only know of the code but be able to reprogram it speaks to his respect for Khan's intellect. He follows up his suggestion that Khan changed the code by saying, "He's quite intelligent."
"He clapped his captain—his friend—on the shoulder. Yes, this man was very much like James Kirk, in all the ways that mattered." --Christopher L. Bennett-- Star Trek: Mere Anarachy, The Darkness Drops Again