갈라서다 = to split up (intentional separation or divorce, or breaking up in some other other kinds of relationship).
이별하다 = to part with someone for good, or indefinitely (commonly in romance, but not always).
작별하다 = say goodbye and part with someone for the time being (may or may not be intentional)
갈라서다 is a practical term describing actions. 이별하다 is rather literary. In daily life, we use 헤어지다 instead of 이별하다. So you hear 이별 in songs and poems a lot, while 갈라서다 is only heard in real life, and 헤어지다 in both.
작별하다 has a much lighter meaning than the others, typically of unintentional and temporary parting.
돌아서다 = turn back (physically or figuratively).
깨지다 = shatter (physical), break up, or go awry.
미련이 남다 = Can't cut the tie completely. Have a lingering feelings for someone after splitting up.
허전하다= Feel empty, as if something is missing.
괴롭다= Feel (emotional or moral) pain. Agonize over matters of relationship or social responsibilities.
서운하다 = Feel sorry. feel regretful (because of a disappointing outcome, to part with someone, etc)
후련하다 = Feel good because you're freed from a difficult situation. (서운하다 and 후련하다 are antonyms)
- 영숙은 약혼자에게서 마음이 돌아서버렸다.
- 남편에 대한 믿음이 깨졌다.
- 사귀었던 사람과 헤어졌지만 미련이 남는다 / 있다.
- 파혼 후에 마음이 허전한 걸 어쩔 수 없다.
- 단짝이던 친구가 이민을 간다니 너무나 서운하다.
- 말썽 많던 직장을 그만두고 다른 회사로 옮기니 속이 후련하다.