Translation:Whose glass of juice is this?
Chinese follows very simple grammar patterns that once you learn, you will sound more like a native. 谁的 is one of them. Sure I can try to put 谁 in the beginning or the middle of the sentence but it would sound weird to a native speaker to do that because it doesn't follow the normal grammar pattern. These characters usually go at the end of a phrase.
Examples: 我的- mine 你的- yours 他们的-theirs 谁的-whose
Not really. The word used here, 杯, is actually used to indicate a cup/glass of juice, like a measure word, rather than a bottle 瓶. To specify a glass specifically, you could use the material it is made of - 玻璃杯, but most of the time specific beverages suit specific receptacles, so it's not really needed.
Typically, in English, we say "whose juice is this?". Almost no one (if not absolutely no one) will say "whose glass of juice is this"? The sentence with "glass" is the "technically" correct translation, yes. However, the purpose of this Duolingo program is not to teach "technical correctness", but rather general usage of another language.