Considering you broke up with him... why do you care? You didn't want to be with him, so why are you interested in what he's doing now? It's possible that he's hurt by the break-up and wants to do something to "hurt you back" or make you jealous (immature, but still...), or he might be trying to get back together with his ex. Whatever his reasons are, you need to remember -- YOU broke up with HIM. What he does now shouldn't affect you; you wanted him out of your life.
Because he wants to add her. Maybe he wants to be friends with her again and see what's going on with her life. Maybe he's stalking her on facebook like you're stalking him. Does it really matter since you guys aren't together anymore?