Re: Do you have ... ? Yes, I have.
I would never say "Yes, I have" as a response to "Have you got a..? ." I would answer "Yes, I do" or "Yes, I have one."
I would use "Yes, I have" if you asked me "Have you read this book?" or "Have you fed the cats?" or "Have you seen this movie?" as a pure axillary verb, but not as the "have" for possession.
I don't know if this is personal to me, or American in general.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.