What date is Parents' Day?

It is May 8th.

What day is Parents' Day?
It is Monday.

Are each answer and question grammatical?

Yes. They are all grammatical.

However your question does not have a subject and verb that "agree". Can you figure out what the problem is?

Are each answer and question grammatical?

Ooops! I didn't see that one. Good catch, Guru.

Yes, both the questions and answers are grammatically correct. However, the answers alone are not sufficient to determine the correct date or day for Parents' Day. To get the correct information, you would need to consult a reliable source such as a calendar, official websites, or consult with relevant organizations.