1). Two ways. First, there's a forest quest series where you try to hunt a fairy, but your slavers get abducted, complete that quest chain, then after a while, it will reappear. Redo the quest chain again, and eventually you can get a different option. Second, it can spawn naturally with a very, very rare chance.
2). Uhh, I just tend to get them randomly, I don't think I've ever found a quest that guarantees one. If there is one, it should be in the desert...
3). I'm not sure if it's guaranteed, but any quest in the desert that mentions the mist is your best bet. They appear frequently there.
4). There is a quest or event that gives you a mindbroken slave with a special title that has a long quest chain attached to it, the end of that quest chain either can, or does give you an angel. I have no clue if these can spawn naturally, like fairies can.