Maybe your BF was in love with her before and hasn't fully got over her or maybe they are just still good friends and like to talk
She can be. Are you comfortable with it? Is she? If both of you are, there's no reason not to be friends.
if he dumps you and then very soon (like in a couple days or the next day or whatever) he is with someone else. especially if it is an exgirl or someone he has been rumored to like.
If you feel you have matured and are more secure with yourself and now believe she is the right girl for you try telephone her (not texting her) and ask her if she will meet you somewhere quiet at one of your favorite places and tell her how you felt back then, but you have matured and want to get back together. You have hurt her a great deal by breaking up with her and whether you felt you were not good enough for her or not she probably thought you were ditching her for another girl. Explain how you felt and why you broke up. Let her know you have been miserable without her. If she is over you or has another boyfriend then ask her if you can at least come and get your things from her place (it's illegal for her not to give them to you if she has not asked you in the past to pick up your things) and then move on.