어 is an ending suffice used for present tense.
밥을 먹어 means
1. I'm eating meal. (declarative sentence)
2. Eat meal. (imperative sentence)
3. Are you eating meal? (interrogative sentence)
V-는 거 is a Noun Form transformed from the verb to be used as an object or an subject in the sentence.
보다 to see (a verb) → 보는 거 seeing (a noun)
영화 보는 거(것을) 좋아해요. I like seeing movies.
밥을 먹는 거야 means "be eating meal."
It is not a full sentence. It depends on the context.
ex) 배고프니까 밥을 먹는 거야.
For I'm hungry, I'm eating meal.