Does this sentence not translate as "I study the literature and the poetry"?
Not really. It's a special case.
It didn't accept "i am studying literature and poetry". really?!? that is plain dumb.
Yes, this is much more natural, and is normally the form in which the answer is given. Duolingo seems to have completely lost the plot here.
Poezia ține de literatură. Adică:
Poetry is also literature
In this sentence we have "studiez literatura și poezia"; in another we had "știam arhitectură și sculptură": shall we use the definite or indefinite forms in these sentences? Whichever the case, one of the two is incorrect.