What if it is about a person who is a manager in school? Why it can't be 'headteacher'?
Headteacher (principal, headmaster) is dyrektor. I think that the course creators either forgot or didn't know this synonym, and it should have been reported.
would be nice if "where is our boss" worked here
We do keep "boss" for "szef". For example, "dyrektor szkoły" (a headmaster of the school) is not the pupils' boss...
His translation should be "acceptable", though not the most common.
Just like Kierownik is more common term than Dyrektor for a manager.
Gdzie jest nasz dyrektor/(szef)? - Where is our supervisor/manager/(boss)?
Gdzie jest nasz dyrektor (szkoły)? - Where is our principal/superintendent/
Does this also translate to the director of films as opposed to just business?
No, that is "reżyser".