Yes she is, she was born at Bamberg County Hospital in Bamberg, South Carolina.
Parental citizenship status is irrelevant.
Wrong.
Jus soli is not enough.
Both parents have to be US citizens
She can try to claim citizenship but she's not a Natural Born Citizen since she was born to parents who were citizens of a foreign country.
https://www.thepostemail.com/2023/01/30/nikki-haley-is-not-a-natural-born-citizen-of-usa-to-constitutional-standards-not-eligible-to-be-president/