This sentence is wrong. "제 남동생은 밥을 거의 다 먹었어요." and "내 남동생은 밥을 거의 다 먹었어." are more natural expressions, and '제' cannot happen together with -아/어.
대부분 is an adverb as well as a noun. there is nothing actually grammatically incorrect about this sentence, despite the honorific mismatching.
대부분 comes from 大部分, which simply means "most" "the majority"
where 거의 means "almost" one could argue 거의 다 and 대부분 are two routes to similar but different meanings
'제' is a formal one, used to an older people. And '먹었어' is 'ate', but this is an informal one. USUALLY USED TO THE YOUNGER PEOPLE. So this is like: "Please, I go now."
I have a feeling this was written by a learner themselves. Which is cool, we all make mistakes. But as stated by ling.ko, it should really be 거의. The current sentence would be more actually translated as "my little brother usually ate food."