Is it correct to say how many is there?

Answer 1

No.

The choice between the phrases "there is" and "there are", when used at the beginning of a sentence, is determined by the noun that follows it.

Same works for a question. "Many" is plural. Therefore it needs the verb "are".

If you are asking "how many", that implies you think there is more than one.

You wouldn't say, "There is many dogs."

When in doubt, try switching the words around as if you are answering your own question:

Is there? = There is.

Are there? = There are.

How many dogs are there?

There are twelve dogs.

Or

How many cats are there?

If there is one cat, the person is going to reply, "There is only one cat" using the qualifier of "only", because they caught the implication of the plural.

Or, you could ask, "Is there only one cat?"

And the answer could be

"Yes."

Or

"No, there are five cats."

Which means there are many kittens the on the way. ; - )