Hi Lilith,
When you ask a question with "any" about the existence of things, you generally use the plural: "Do you have any books?" You are asking if the person has even one (but maybe more) books.
You can also use it to ask about uncountable things: "Do you have any milk?" Because "milk" is uncountable, we don't generally use a plural form like "milks".
You can use "any" with a singular noun when you emphasize that you are not referring to one particular thing: "When I said I don't like your family, I wasn't talking about any particular relative of yours. I just don't like any of them."
And you can use "any" with a singular noun when you are emphasizing a wide range of choices: "You can choose any book you like from the library." Or: "Can I really visit you at any hour of the day?"
I hope this helps to answer your question.