both forms are correct. but I think the "have got" pattern is generally the preferred form in British English while most speakers of American English employ the "have". "do you have a dog?" (American) "have you got a dog? (British) :)

I'd have to say I don't have a dog to either question. :P

Both are ok

No difference whatsoever.

no difference do you have......?= have you got.....?