1

These 2 both look correct to me:

What date is it in China?
What date is today in China?

Is any of them better than another?

2

What date is it in China?
What date is today in China?

both are correct and understandable.
Your first sentence

What date is it in China?

would usually be understood to be asking about today.

More idiomatic may be

What date is it today in China?
What is today's date in China?

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