I'm wondering about the translation. It seems to me that "are there" is not part of the original meaning. Wouldn't "how many cats?" work as well?
"How many cats?" Without the "are there" would be just "कितनी बिल्लियाँ?"
How many cats, should also work. But it's a phrase not a compete sentence in the technical sense. Maybe that's why they added 'are there'.
Certainly as a standalone sentence. But in a hypothetical conversation you could get something like this: "There are dogs, cats and horses." कुते, बिलीयों और घोड़े हैं। "How many cats?" कितनी बिल्लियाँ हैं ?
We can't equate the rules of grammar with the colloquial speech. Grammar is relatively fixed while speech can be any which way.
When we speak, we dont care about subject or verbs as long as the meaning is clear. That's why phrases are fine in colloquial speech. But English grammar dictates that a sentence must have a subject and a verb. It can have other aspects but to be called a complete sentence, it must have a subject and a verb. If it misses any of the two, it becomes a phrase. And by that rule, "how many cats" can never be a sentence because it lack a verb. Of course we use tons of phrases in our daily lives and this is just one of those.