Although all 3 are very close to correct I would make the following changes: 1. Just say "What is today?" 2. "Do you know what today is?" Like in number one the repetition of day is unnecessary and sounds a little awkward. 3.Follow Amy_lin's suggestion and say, "What day is it today?" The verb should come before the object, in this case "it".

What day is it today?

All 3 questions are correct, and the answer is correct.

yeah they sound right. what is "children's day"?