Here's a short description of each.
1. ~며 and ~면 - verb connective conjugations
* -며: expresses parallel actions (음악을 들으며 공부를 한다: study while listening to music).
* -면: expresses a conditional (지금 가면 다시 못 온다: If you go now, you can't come back).
2. 대 and 되/돼 - verb forms at sentence endings
* -대: short form of the ending -다고 해(it is said that ...). 아빠가 돌아오셨대 (Father is said to have come back)
* -돼: ending form of 되다 (become, 되다->되어->돼). 물을 얼리면 얼음이 돼 (If you freeze water, it becomes ice).
3. 싶은데, 싶지만, 싶으니까 싶어서 - 싶다 in ~ㄴ데, ~지만, ~(으)니까, ~어서 connective forms
* 싶은데: 싶다 + -ㄴ데(soft "and" or "but"). 가고 싶은데 돈이 없어 (I want to go, but I have no money).
* 싶지만: 싶다 + -지만(strong "but"). 가고 싶지만 돈이 없어 (I want to go but I have no money).
* ~으니까: direct and clear reason. 돈이 없으니까 못 가 (I can't go because I have no money).
* ~어서: 1) reason/background, 2) a means or required action for the following action/event.
** 1) 돈이 없어서 못 가(I can't go because I have no money - direct reason).
** 2) 생선을 구워서 먹었다(We roasted and ate the fish - "roasted it" (so we can eat it), then ate it).