Hi Dan. Well, as you could tell from my post, I'm not very good at this romance thing. But if you think I share somewhat the same thought pattern as this girl, I can give you some insight.
About why she suddenly gets mad at you: When I get mad at the boy I like, it's because I think he takes me for granted. When he's affectionate, I just start thinking, "Yeah right, he's probably like that with all the other girls he knows." Or "He's just playing with me." Maybe you should be a little less flirtatious? Also, do you have many other female friends? My guy does and I bristle at the thought that I am "just another one of those".
Running off to other guys is what girls do to make you jealous. I don't do it because I don't want to hurt my sweetheart, but it has crossed my mind many times. Girls figure, "He'll realize how special I am and how much he wants me if he imagines me in someone else's arms."
As for being told that she likes some other guy, who told you that? Because that is another hare-brained scheme that I thought of to make my guy jealous. A friend volunteered to tell him that I like someone else. Of course, I never went through with it, because I didn't want to hurt him.
Joking around and not getting anywhere: He and I are always joking too, always playfully chiding each other. We're famous for our verbal sparring. But sometimes I wish we could actually *talk*. Heart-to-heart. I want to be an important part of his life, and I want him to be involved in mine. I guess my insecurity also comes from the fact that he's in university and I'm still at high school. He has his own circle of friends, his own social life, I hardly see him, rarely know where he is, what he's doing.
Anyway, if I were in this girl's shoes, I would just want to be assured that you love me and care about me no matter what. Take extra interest in her life, her feelings, her family. Girls ESPECIALLY want to talk a lot about feelings and emotions. And you have to be very understanding there because they're usually afraid they'll just drive you away. Appreciate all the special little things about her: her hobbies, her talents, her quirks, everything. Share stuff about yourself that you normally wouldn't talk about to other people. Oh, and send her flowers and small gifts ("Thought you might like this."). Let her know how important she is to you.
Good luck!