Hi
Q: Do you want to sing a song?
A: Yes
Q: What song do you want to sing? or Which song do you want to sing?
Best Wishes
Q: What song do you want to sing? or Which song do you want to sing?
I don't think there's a definite rule. In this usage, what song would be the more general question, offering the choice of any song at all. Which song would indicate an offer to choose from among a (more or less) limited selection.
They're both correct. Which song suggests a song from a limited selection to me, and what song could be any song.