Это is used regardless of gender if you are specifically saying something meaning "this is.." as it is the demonstrative pronoun. It cab also be used as the neutral non demonstrative pronoun for a sentence like "this apple", but be careful because without context "this apple" and "this is an apple" will appear the same in Russian. In this case, as "girl" is feminine, we can be confident in knowing that зто is being used in a way to say "this is a" which is distinct from just saying "this..."
It has to end in -a because it is being use in a nominative case function (subject/predicate) in the sentence, and -a is the feminine singular nominative case form for девочка. When you change the ending of a word, you change the case or number (singular/plural) or both, and there has to be a reason for doing that, such changing the function of the word in the sentence by, say, using it as the object of a preposition like в or на. With either of those prepositions девочка is changed to preposition case девочке.
In Russian they don't have a word for "the", so "this" is talking about a specific girl. In a sentence in which you are asking where she is, it makes sense to accept "the" which is specific without indicating where she is. My assumption is that "this girl" is somewhere close by, hopefully in the house, while "that girl" could be anywhere.
I agree. In this instance, "the" is very specific, acting as if it were "this", as if the speaker is pointing to a specific girl. It's very different from asking something like, "Where is the butter?", where any butter will do.
Perhaps, though, "ето/a" would be appropriate for something like "Where is the garlic-butter"?" or "Where is the milk I just heated up?"
The English sentence is actually fairly odd. "This girl" signifies a very particular person, but the context doesn't suggest anything warranting such strong focus on the girl.
Is Duo simply using various forms of это to help teach us the basics of case/gender/number? Or do Russians have a particular meaning they attach to the determiner это which is somehow lacking in English?
Because we did not start by practicing the sounds of letters and groups of letters extensively i find these oral exercises a waste of time. I cannot pronounce the words. The course needs to focus on the very basics of the sounds for westerners who have no previous experience of the language.