While in in English the article "the" is optional (i.e. I love music, or I love the music) in Greek it would be awkward without the article "την".
Could you use this to refer to a specific opera like one could in English (ie. "Are you familiar with Carmen? Yes, my aunt loves the opera?") or does it just mean that she likes opera in general?
I guess it could, depending on the context of the conversation. In this case, where there is no actual conversation and the sentence is all by itself, I would assume the the speaker is talking about opera in general. ^.^
yes but here we're using the definite article, so the hint "a" is not only wrong because it should be "an" but also because it has to be "the".