can だ be placed after an い adjective? I learned I shouldn't but I see it often online

Confusing uses of 하는 걸/하는 듯 What does it mean when some (seemingly) random 하는 걸 pop somewhere? as in "그대와 나의 눈빛이 말해주는 걸" "나는요 오빠가 좋은걸" about 듯: I learned it as meaning as if (eg. 모르는 듯 아무 말도 안했어) but it seems like it has different meanings like "그게 더 괜찮은 듯" I've been having these doubts for a while :-( Please answer me!

What does ~치 않다 mean and when should I use it (If I should at all) I've been seeing it all the time but I never really cared but now I'm pretty curious is it the same as 지 않다? If so, then why don't people just say "지 않다"? eg. "애가 원치 않아" = "애가 원하지 않아"?

In the sentence 食堂の食べ物はあまり好きじゃないんだ。 what does that ん mean? Also the same in 夢があるんじゃないか

What does -지 actually mean? Many sources say -지 (as in 이쁘지?) means right? but there are some sentences where it just doesn't work like that, for example a comment on youtube said "어떻게 저렇게 부르지?" It just doesn't make sense. So, could someone please show me the meaning of -지 in detail? 미리 감사합니다

How to say "I know, right?" or "Same!"?

Quoting when there doesn't seem to be any quoting? Sometimes while watching something subbed, I come across some things like "난 두렵지않다고" for "I'm not afraid" even though the person hasn't said it before. So.. why is that?