You can use either of them. They are both gramatically correct. It seems "Do you have any" is more often used, although the other one sounds more elegant. "Have you any idea ...?"

Both are correct, though I guess "have you any" is used more often in the UK. "Have you got any" is also correct and common, but with an extra meaning. In most cases you can use it in place of the first two phrases, but "have you got any" implies an acquisition sometime in the past. People are often careless about this (I have / I've got) so take note. :)

I think that it may be a good idea to hear some context regarding the question.

Many thanks for all! Yours answers are useful for me!

Both are correct. Cherry is right, though that, "do you have any" is more often used. I actually prefer to use"have you any?" though.