1. "~하든 말든" means "whether they do it or not" (in this case, it's "whether they stare at me or not")
2. "토라지다" means "being pouty" So "토라진 척하였다" means " I pretended to be pouty"
3.
-"오래비" can mean different things depending on the context. The direct translation would be " older brother", but a male friend sometimes might call himself "오래비". It's an important point, because other people will never call him "오래비" when he's not your real brother. It's kind of a playful thing between friends/lovers. I can't be sure, but in your sentence it's highly probable that "이 오래비" refers to the person who's saying it(he's addressing himself).
-"피" is just an exclamation, like 'pff'.
-"졸졸" is an adverb, and it's often used in an expression "졸졸 따라다니다" that can be translated as " following around". But "뒤를 밟다" means "stalking", so the person addressed in the sentence was following the speaker secretly.
-"야단" means "fuss" The whole sentence can be translated as "why are you making a fuss following me around?"
-"차이면" is a variation of a verb "차이다". It can have two meanings, "dumped (by a boyfriend/girlfriend)" or "kicked". Can't be sure without the context. I think there is a possibility that neither of them are right. I really don't know what it could mean.
Sorry for any mistakes in english grammar/phrases!