Does John Bolton have dual citizenship?

Yes you can receive both of his dual citizenship.

Yes. Currently, a U.S. citizen can apply for citizenship in another country (i.e. Naturalization) without losing U.S. citizenship. A person with a US citizenship can become a citizen of another...

No husband has to apply again for himself because shared visa like spouse can be granted or extended but not the citizenship for an individual.

India does not allow dual citizenship. But you can apply and get a passport-like booklet, at the nearest embassy and consulate general, that will allow you to travel to India visa-free.

Yes.