Answering number one is really hard for me. I've avoided relationships and friendships so much, that I'm not sure what the real answer is. Well, actually, I have no interest in romantic relationships (not an avoidant thing, just asexual, so while I have dated in the past... it's not something I ever actively pursued), and I have avoided friendships in the past several years. Thinking about the few friends I do have, though, I'm more afraid of abandonment, and I worry most about it when I have to confront them for whatever reason. Such as voicing my opinion, or standing up for myself. I will do it, but I spend a while afterward worrying that they'll abandon me.
Number two... When I'm called on in a class or work setting. Even if I know the right answer, I feel incredibly awkward having all eyes on me. Just thinking about it makes me feel awkward, actually.