대 comes from the hanja 'big' and 부분 means 'part' so 대부분 means 'majority' or 'the most part of something'
Why is 대부분 after the noun it describes?
It can come before or after. I haven't noticed if it happens more one way or another though. If it comes before you can add ~의, like 대부분의 지역 (most of the region), but as usual the article is often dropped as well.
Doesn't Korean put descriptions of quanity after the noun, such as using numbers followed by a counter word? I think 분 is also a counter word, so maybe this is the same.
It looks like it reads "we want to go for the most part" where 대부분 reads as "for the most part"
If 대부분 comes after the noun, do you not have to use a particle on the noun anymore?
Why is "우리는 대부분 가고 싶어요" wrong? Can you not put a topic marker after 우리?