There are fundamentally 3 kinds of "ANY" in English:
1) "ANY" meaning "AN UNDEFINED QUANTITY OR NUMBER OF SOMETHING":
a) If it's referred to an UNCOUNTABLE noun (which has no plural), obviously that noun will be in the SINGULAR, so you will say for instance ANY BREAD, ANY MILK, ANY INFORMATION, etc;
b) If it's referred to a COUNTABLE noun, you will use that noun always in the PLURAL: you will say, for instance, ANY QUESTIONS, ANY CIGARETTES, ANY EGGS, etc (note that actually the SINGULAR forms of "ANY" (and of "SOME") with regard to COUNTABLE NOUNS are "A" and "AN" : A QUESTION, A CIGARETTE, AN EGG, etc);
2) "ANY" meaning "IT DOESN'T MATTER WHICH" of a certain group of things: with this "kind" of "ANY" you will use the nouns in the SINGULAR form, for instance: TAKE ANY BOOK YOU WANT;
3) "ANY" meaning: "EVEN A SMALL AMOUNT": you can easily identify this "kind" of "ANY" because it goes always with COMPARATIVES: for instance: "IS SHE ANY BETTER?", meaning "IS SHE BETTER EVEN, AT LEAST IN A SMALL AMOUNT?"
There are other little "shades" of meaning, but I think the ones above are the most important forms of "ANY".
So, to recap: 1) a): WITH SINGULAR NOUNS; 1) b): WITH PLURAL NOUNS; 2): WITH SINGULAR NOUNS;
3): WITH COMPARATIVE ADJECTIVES.
You should identify the "kind" of "ANY" from the context and the kind of sentence: for instance, in your example, "ANY" is clearly 1) b), and it comes with a PLURAL COUNTABLE NOUN: "if you have ANY QUESTIONS" (meaning: if you have a certain number of questions...
An example of 2) kind of "ANY" might have been: "ASK ME ANY QUESTION WHICH MAY COME TO YOUR MIND (meaning: WHATEVER QUESTION of the number of questions which may come to your mind, it doesn't matter which).
I hope this helps!