SO,both is valid stence with the silmilar meaning and a little difference.
JUST LIKE:
"Are there any men in our world more famous than George Bush and Tony Blair?"
AND
"Is there any man in our world world more famous than George B
Ｄｏ ｙｏｕ ａｇｒｅｅ ？
ｓｏｕｒｃｅ ｏｆ ｓｃｅｎｔｅｎｃｅｓ ：
'Any' is effectively an adjective in this use, so it does not determine the number of the noun following it at all. The number of the noun is determined by what you want to say, naturally.
So, for example:
"Are there any men in our world more famous than George Bush and Tony Blair?"
AND
"Is there any man in our world world more famous than George Bush?"
are equally valid sentences. The choice between singular/plural is simply determined by what it is you want to say.
P.S. Kate B is perfectly correct in saying "Are there any questions" is a valid sentence in English. In fact, your objection that it is incorrect despite being frequently spoken and accepted is a logical fallacy, since the only criteria for a sentence's validity Linguistically speaking is whether it is acceptable to the native speakers of the language.
