Sort of between the two. If I had to write it in English I would write it as 'ng', as in the 'ng' part of a word like 'hung' or 'ring'. But it's hard to put into English sounds as Korean sounds are not quite the same. I highly suggest not romanising hangul into English when learning. Learn all the individual sounds first and it makes learning Korean so much easier.
try to say it with you mouth closed, it's more like a sound instead of a word, like when you do mmhm yk
It is the same but when you talk to someone older (like your teacher, parents...) you use 내 (nae) and when you talk with someone who is as same age or younger than you (your friends...) you use ㅖ(ye).
No , there's no difference but maybe they mean 안녕하세요 (annyeonghaseo) means hello and 안녕(annyeong) [which is the shorter way of annyeonghaseo] means hi.