'The team captain' would also be correct. Although it is more helpful to think of this phrase as meaning 'Captain of the team ' because most times you use ' of the ' in English this will require the use of the genitive in Irish i.e. The name ' of the ' street, The colour ' of the ' car or The top ' of the ' pen.
@Fergall, Yes. Technically it is "the", but in English, in this case, 'the' is not needed.
He is the captain of the team = he is team captain = he is the team captain = he is captain of the team.
The thing it is never is anything meaning 'a team captain' or 'a captain of the/a team'.
For the latter, or if you wanted to emphasize 'the', yoy would need to use other constructions...
Why do they ask for the genitive form of foireann which has not been introduced at this stage of the Irish course? How can I be supposed to know that?
Probably because very frequent concepts have to be used before they are introduced. Experiencing them is no harm, and it would be hard to avoid it.
No, but “the captain of the team” would be correct, since the na makes both captaen and foirne definite.
Then how would one say "a captain of the team" (in the case of there being co-captains?)
Captaen den fhoireann, using the partitive dative rather than the genitive.
It's in the genitive. Some nouns genitive singular forms are their nominative plural ones. foireann is one. Also, because it's a feminine noun, you use na as the article in this case.