Khan was trying to run a ship usually crewed by at least 300 with a crew of about 60. Even Enterprise with a full (admittedly mostly cadets/trainees) crew faced huge damage-control issues.
Where are those numbers from? not that it matters much, the next movie canonized that a chimpanzee and two trainees can run a starship.
After being modified by Mr. Scott. And even then it was useless in combat.
They had surrendered. They weren't expecting to fight their way to the bridge or anything.Not only that, the commander of an enemy ship with about twelve men thought they could board and overtake it.