Anyone is undoubtedly singular and “Anyone knows” is the correct answer.

Does anybody know or do anybody know?

Do you know why 'Does anybody' is correct? 'Anybody' is a third person singular form and takes -s in the present simple tense. That's why the question form requires -s and 'Does anybody' is correct.

Which is correct know or knows?

"Knows" is the singular, present-tense form of the verb. I think he knows exactly what you mean. However, there are certain sentence structures where "know" will be used with a plural form against a singular subject: How did Jacob know what you were planning?