"She has not eaten the soup yet."
Translation:Вона ще не з'їла суп!
This is a direct object, so it's usually in Accusative as a whole. You may use Genitive here only if you mean eating a part of soup: Вона ще не з'їла [анітрохи] супу — She has not eaten the soup yet, not even a spoon of it. Я з'їв [трохи] супу — I have eaten some soup. You don't have to say words in the square brackets (then it's better to say поїсти instead of з'їсти), but Genitive implies something like that.
The genitive would be супу, not супа.
Both суп and супу work in this sentence.
Right! We always use the verb їсти (eat) about soups, never пити (drink).