1. John has a book, doesn't he?

Question

2. John has a book, hasn't he?
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Is #2 used in British English?

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3. I think he is serious, isn't he?
4. I know he is kind, isn't he?
5. I believe she isn't diligent, is she?

6. I think he is serious, don't I?
7. I know he is kind, don't I?
8. I believe she isn't diligent, don't I?
(What about these ones? Which ones are correct?)

Answer 1

Yes, 1 is American English and 2 is British English.

None of the rest are normally used in English, British or American. Here are some that would be:

He's serious, isn't he?
She's a kind person, isn't she?
They work very hard, don't they? (sub for "diligent")

The tag question is asked about the person(s) being described, not the person with the opinion.