I thought his wife Mara was the science officer?
Yes, Kang introduced Mara as his science officer. Mara was the only one who stayed in the transporter room with Kang when he delivered the introduction.
You are born into a class. Can't move in our out of it.
You're thinking of a caste. There are many cultures in which a social class can be moved into or out of -- the United States, for example (although many in the American upper class are trying to make it harder for others to move into it).