Is/are there any question/s?

I woke up this morning to a interesting text message.  It asked about the peculiar feature of the English language shown in the two example sentences below:

1. Let me know if you have any questions.
2. I'm sorry for any inconvenience.

You'll notice that in the first statement, the noun following "any" is in the plural (questions), but in the second, it is in the singular (inconvenience).  Why should that be?  Mightn't it be just as proper and make just as much sense if these sentences read as follow?

1a. Let me know if you have any question.
2a. I'm sorry for any inconveniences.

If you're a native speaker of American English, then these sentences surely sound odd to you.  Additionally, you might have been reminded of any of the following common phrases.

1b. Is there any question (that)...?

Perhaps you've discovered that the usage of "question" in instance 1. differs from the usage in 1b.  In the former instance, the word refers to "a sentence worded or expressed so as to elicit information."  In this sense, "question" is a countable noun.  That is, he has two questions, but I only have one.  However, in the latter instance, this same word refers rather to "a doubt about the truth or validity of something."  Here, "question" is less concrete, more conceptual, and (althought technically countable), less apt to be counted in the same way.  Now see this.

2b. The inconviences of rural living can wear on aging people.

Here, "inconvenience" in instance 2. refers to trouble caused, whereas the instance in 2b. refers to instances of such trouble.  The line is indeed blurier, but still there somewhere.  Below are a few other fun examples, just to push the point a little further.  These examples are not consistent in terms of usage differences, but they all still illustrate a point I make earlier about countable and uncountable nouns.

3. I don't see any glass.
3a. I don't see any glasses.

These are totally different words.  The first "glass" is an uncountable noun.  Now that you've swept up, there is no more glass on the floor.  The second "glasses" can be both an inherently plural noun, referring to eyeglasses, or it can be a countable noun in the plural, as in wine glasses.  This sentence could have either meaning.

4. Do you have any money?
4a. Have there been any monies exchanged?

Here, "money" refers to a medium of exchange, whereas "monies" refers to discrete sums of money.

5. Is there any soup on the menu?
5a. Are there any soups on the menu?

The first example here also can have two meanings.  Do you see?  The second is more specific, asking about the existence of a soup or variety of soups listed on the menu.

Hopefully, there isn't any question that I've made things clearer, but if there are any questions, please do let me know.