I got your point but I don't think that is totally wrong. In a normal conversation or situation with your counterpart, when you say this, it means "how much money do you have?". If you wanna say "how much money is there" in Korean, that would be "돈이 거기에 얼마나 있어요?". However yes, the context will be needed for more accurate translation or your answer should be accepted.
"There" can mean (at least) two different things in English. It can refer to a location, which can be 거기 or 저기 in Korean, but when combined in a specific way with the verb "to be", it actually means to exist, and doesn't refer to a location (though a location can be specified). "How much money is there?" is a form where "is there" means "exists" and does not refer to a location, so instead of 거기 or 저기 we just translate it with 있다.
In the interrogative form of "to be there" (meaning "to exist"), some form of the verb "to be" usually comes before the word "there"--some examples:
"How much money is there?"
"Are there any books in the library?" ("In the library" specifies a location but "there" is just part of "are there" which is asking if they exist.)
"Why isn't there an easier language?"
In the declarative form, some form of the verb "to be" typically comes after the word "there":
"There are 26 letters in the English alphabet."
"There's a snake in my boot!" ("There's" = "There is")
"There wouldn't be life if there wasn't carbon." ("wouldn't be" and "wasn't" are two different negative forms of "to be", one is called "conditional form" and I don't remember what the other is called--maybe "subjunctive," not sure.)
None of these would ever be translated with 저기 or 거기 because they're really just an idiomatic English way of saying the same thing as 있다.
That specifically means to be carrying, to have on your person. It could probably be used if that's what you intend to ask. If you're wondering how much money someone has in their bank account (or the total amount of money they earn), then 가지고 있다 is incorrect because it means "to be carrying" or "to have on your person."
It is not. In many Asian languages, the pronoun is often omitted as it becomes obvious who is involved in the conversation. If I asked you this question, you'd know that you're the addressee. The idea is not foreign in English either, as you'd say "got home late", or "want some chocolate?"—you just know who the sentences refer to.