[evil_twin]

1) I'd just fold. Ideally you want a multiway pot with position in order to play this. The problem with raising this when it's been folded to you is that unless only the BB or SB call then you're likely to be playing a raised pot OOP with a crap hand... not ideal. Of course a raise is fine sometimes, but it certainly wouldn't be my standard play.

2) You're on the button with AJ? Well, a raise is probably in order. The issue that often arises here is that because it's been folded to you and then you raise on the button the blinds assume you're full or crap and call/raise. This isn't so bad since you have an OK hand with position, but without care one can find yourself playing a big pot when you didn't really want to. I'd like to hear the better players view on this situation.