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.)

Am I correct in thinking that "Скільки там студентів" means "how many students are there [in that specific place]" and not "how many students exist"? How would you translate the latter into Ukrainian?

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?"