Does "muzyka popularna" simply refer to music that happens to be popular, or does it also refer to "pop music" as a genre?
a bit of both. popularna muzyka is music that happens to be popular. Muzyka popularna is a genre, but I think it is wider than pop.
As far as I know, in polish musicology "muzyka popularna" is a term that describes all music that isn't classical and contemporary (classical) music.
So...is "You listen to pop music." actually incorrect (as reported in the test) or just "not as correct" as the alternative?
I suspect the words have exactly the same meaning in both languages. Even classical music is referred to as popular when the most popular pieces are played (think Class fm radio and light classical music), but the English 'pop' is only an abbreviation that has come to be used for the 'Radio 1' genre. There is probably a similar abbreviation (the same?) for the equivalent music in Polish.
Same, pop. "Słuchasz popu", sometimes "Słuchasz muzyki pop", "Słuchasz muzyki popowej".
Słuchaćrequires Genitive - that is how Polish works. The question for słuchać is kogo? czego?(GEN) - słucham nauczyciela, słucham muzyki, NOT kogo?co?(ACC) słucham nauczyciela, BUT słucham muzyka. In this case słucham muzyka means I listen to the/a musician (muzyk), not music(muzyka).
Bottom line : słuchać + GEN.