Yes, if you hear this sentence being spoken, it most likely is the case that the word being used is isst and not ist. In other words, Sie isst eine Tomate ("She eats a tomato") generally makes more sense than Sie ist eine Tomate ("She is a tomato").
However, there is no way to differentiate isst and ist by speech alone. Also, Duolingo has many other (and much stranger) examples of sentences without context. As a result, it would not be fair to say that Sie ist eine Tomate is incorrect if you're being asked to type what you hear because there is no way to tell that it's incorrect without more context. Of course, we can assume the more likely context, but there are always exceptions.
The Sie alone could allow the translation with she, they or the formal you, but the inflection of the verb restricts it to she.
„Sie essen…“ would either be they or the formal your – these two versions are equivalent except for the capitalized pronouns in the formal you form. So if the pronouns is at the beginning of the sentence, these two are both possible.
This depends on the grammatical case as well as the grammatical gender of the noun: Inflection table
neuter noun, accusative case („direct object case“):
„Sie isst ein Ei.“ – “She's eating an egg.”
feminine noun, accusative case:
„Sie isst eine Tomate.“ – “She's eating a tomato.”
two masculine nouns, once with nominative case („subject case“) and once with accusative case:
„Ein Mann isst einen Apfel.“ – “A man is eating an apple.”