The hint also gives "üzgün" for "sad" but my answer "Üzgün şarkıyı dinlemek istemiyorum." was not accepted.
üzgün is only for a sad person
As far as I can tell, "üzgün" is used when you could use "depressed" while "üzücü" is used when you could use "depressing." English just doesn't make the same distinction for "sad" as we do for "depressed/depressing"
The 'to' is implied with the verb 'dinlemek', as opposed to just listen or hear, right? In Dutch, we luisteren (listen) sad songs, not to them, so this construction feels a bit strange.
In English you always listen TO something