difference between any + singular and any + plural (any question or any questions)

any + plural: (any stamps - ямар нэгэн маркнууд) to refer to an amount or a number of something - 
used with uncountable or plural nouns in negative sentences and questions, after if or whether, and after some verbs such as prevent, ban, forbid, etc. to refer to an amount or a number of something, however large or small
       ----- Are there any stamps?
       ----- She asked if we had any questions.
       ----- You can't go out without any shoes.
any + singular: (any bus - аль ч автобус байж болно) to refer to one of a number of things or people, when it does not matter which one
used with singular countable nouns to refer to one of a number of things or people, when it does not matter which one
        ---- Take any book you like.
        ---- Any color will do.

any questions or any question

• They should say, “Any questions?” “Any” is used in a question with a plural or uncountable noun.

• "Any question" places a strict limit on the number of questions allowable to exactly one. For example, there was exactly one question as to who wore the pants. However, where the number of questions has not been determined, or is unrestricted, then the plural should be used.                                                                                                                                               Is there any question that I am correct? I don' think so. (The only question might be "are you correct".) However, any questions you have should be added to the comments below. (Questions might be "are you serious?", "what authority do you cite?", "why is your speellling so bad?" and so forth.)

• If you explain something at a conference (for example), in the end you would say "Any questions?".
  I think the reason is that there isn't a definite number of question you expect to be asked, so you use the plural.
  Honestly, I can't recall hearing/reading "Any question?" used in this way, plus there even is a Radio Programme called "Any questions?".

• Using "any question" sounds so strange.

  "Call me with any questions you may have".

  Yeah, it still sounds better in plural. Though thinking about it, even though it is not a question, it works in the ambiguous or uncertain tense that "any" works with... which is generally plural.

  "Do you have any cats, hats, tires, fires, mice, etc"

  They all run in plural.
  However at the beginning of a sentence, in a more certain, assertive, authoritative tense, singularity is fine.

any idea or any ideas

(is there any difference between "any ideas?" and "any idea?"? (just an example))

• I do see a difference between the two.
  Ex. "Does anyone have any ideas how we can get more customers?" (Are there any thoughts on how we can get more people to use our services?)
  and
  "Do you have any idea what could have happened if you had done that?" (Do you realize what the consequences would have been if you had taken that course of action?)
  Hope this helps.

• 'Any ideas' is fine because the questioner wants to know if 'you' have more than one idea about the business plan.