Yes, or a representative. The indefinite article sounds a bit weird here, I think, and makes me think of him as a representative for his country.
An agent/spy is either called en agent or en spion.
I think "his own country" should be accepted as well. Actually, I think it is more correct. There is no ambiguity in the Danish sentence (whose country?).
Isn't it that a profession doesn't require a definitive article like: Jeg er lærer
This profession has an expansion here, "for sit land", so using an article here is more common. But still not required, you are right.
I don't think that the Danish term "agent" is probably translated in most Duolingo sentences. As the German word "Agent", the Danish term "agent" should be translated as English "spy", not as "agent". This seems to be a false friend.