You're translating "그" as "the" in half the sentences.. either stick with a uniform sentence structure, or let people be right by omitting "그" / "the" which seems more natural anyway.
how come the answer is 그 여자는 그 식사를 해요? not 먹거요? It's my first time learning this and I'm really confused. :(
They keep translating things oddly. It should be 먹어요. The sentence "그 여자가 식사를 합니다" literally means "That woman does the meal". Plus it should be 여자는 not 여자가. This isn't a good site if you're wanting to learn Korean.
Actually, "식사를 합니다" in itself is the action of eating a meal, and that's why it's wrong to interchange the verb stem to '먹다'. If you were to have "식사를 먹어요." in same sentence, it would be like saying 'eat' twice.
EDIT: Also, 는/가 doesn't matter in this subjective case.