You have a weak boyfriend who is so sad that he would continue to talk to a girl that cheated on him. He's still emotionally attached to her and that's not very good for you or your own emotional health. Frankly I think you did good on telling him it's either her or me. You can see how much he is fighting for her still, even though he removed her from his FB. I think you should seriously consider remaining with someone who still skypes with a girl that cheated on him.
Just how long after he broke up with her did he start dating you? He's definately not over her yet, at the very least he loves the attention she's still giving him which is totally disrespectful to you. Are you a rebound?
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion