Question

1. When did the Eleven Cities Tour take place in 1997?

-It took place on January 4.

2. What was the date of the Eleven Cities Tour in 1997?
- It was January 4.

3. What was the date of the 1997 Eleven Cities Tour?
- It was January 4.
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Are the questions and the answers grammatical?

Answer 1

All are grammatically correct, yes.

For the first question, though, I'd rephrase this way:

In 1997, on what date did the Eleven Cities Tour take place?