Using "any" and "a" along with "there is"

Solution 1:

I think we can't use Any like this because it's a determiner and a pronoun used to refer to indefinite or unknown quantities or an unlimited entity.

Referring to Any - English Grammar Today - Cambridge Dictionaries Online:

Any as a determiner has two forms: a strong form and a weak form. The forms have different meanings.

  • Weak form any: indefinite quantities
  • Strong form any meaning ‘it does not matter which’

Warning:

We don’t use any with this meaning with singular countable nouns:

Have you got any Italian cookery books? (or … an Italian cookery book?)

Not: Have you got any Italian cookery book?

And referring to Some/Any from "A guide to learning English":

  • In general, any is used in negative sentences and questions:

I didn't get any nice presents for Christmas this year.

I looked in the cupboard but I couldn't find any biscuits.

I don't need any help.

She's so rude. No wonder she doesn't have any friends.

So in that type of questions the use of a is more appropriate than any because we're dealing here with singular countable nouns.

So the right statements are:

Is there a car in the street?

or

Are there any cars in the street?

Solution 2:

Could you give an explanation why ANY is not used like this:

  1. Is there any car in the street? 2) Is there any book on the table?

No explanation is required at all because "ANY" is used exactly like that.

A: "Pass me my dictionary; it's on the table."

B: "There's no dictionary on the table."

A: "There has to be! I put it there."

B: "There's no dictionary."

A: "Damn! Is there any book on the table?"

B: "Yes, there is a copy of "Little Women".