"A woman is eating an egg."
Translation:Eine Frau isst ein Ei.
No. The case is accusative and Ei is neuter. It can only be "ein". If Ei was a masculine noun, then you would have to write "einen" in this case. See this link:
Why is word order important for this sentence? From what I read, as long as the verb is in the second position of a declarative sentence, you can switch the placement of the subject and object around.. yet "Ein Ei isst eine Frau." was marked wrong. Is it because both indefinite articles for each word stay the same in the accusative case so you can't tell who's eating who?