Re: What is Carol's official position on the five-year mission?
I think red was ship security and weapons in TOS. Security Chief Giotto wore red in "Devil in the Dark". Of course, it could be since gold shirts are probably trained in weapons strategy and tactics as part of command training, they would be the bridge officers in charge of weaponry. Being a scientist (probably an engineer in at least some capacity) specializing in weapons development, it seemed to me Marcus's best fit was with the red shirts.
You're assuming that security and weapons are the same thing. Giotto was security chief, but I don't think he was ever mention of as being in charge of weapons.
Carol is a physicist, not an engineer.
The boring one, the one with Khan, the one where Spock returns, the one with whales, the dumb one, the last one, the one with Kirk, the one with the Borg, the stupid one, the bad one, the new one, the other one with Khan.