Acc to duolingo rules the translation should be as more closer to the original as possible. So "Скільки там студентів" means "how many students are there". "how many students exist" even en english means the quantity of all students in the world, that is why it is not corrrect
скільки існує студентів = how many students exist
If someone ask me "how many students exist" my first reaction is: Where? In US? In UK? or in Ukraine?
What about a conversation where the location was previously decided? In English you could have a similar situation: "I went to school in Texas." "Oh, how nice! How Macy students are there?"
For that reason "Скільки там студентів" is the rght question. To be more correct, your whole phrase: "Ого, як мило! Та скільки там студентів?"
Does the placement of "там" make any difference here? That is, does "Скільки там студентів" sound more natural than "Скільки студентів там"? (Both are accepted as correct by DuoLingo.)
Would it be possible to translate this as, "How many students are there there?" For instance, I presume that "Скільки тут студентів?" would mean "How many students are there here?"