Why doesnt 근처 work here? Because it doesnt have the -ㅔ particle?
근처 actually means in vicinity, not specifically means near/close by.
근처에 should also work
Its common in spoken korean to drop almost all particles in shorter sentences
Why isn't there a particle of some sort on 여자?
The 가까이에 works as such. The particles just help you describe the things in the sentence, so adding a position will do the same job.
I read that there used to be (and you still can use it) posessive -의 attached to the nouns. That would mean that the boy sits in the woman's "closeness" or, in other words, close to her.
is 남자아이가 also correct for the subject?
Really... just the "에"...
hello. whats the difference between using 가까이에 and 가까에
why does "남자아이는" not "남자아이가"?
It could also be 남자아이가. Both -는 and -가 mark the subject.