Re: Do you have + article + singular or Do you have + any + singular?
I'm sorry, but I don't want to answer this question. Why would you ever be pressed to choose from two unnatural questions, when there is a perfectly natural alternative.
Don't fill your brain learning which is the "less bad" of two bad choices. Learn the natural construction -- which you have clearly already done -- and move on.
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.