Nothing in your past relationships are germane to your current/future life except what you thought and felt (since it's your life). No way your ex-girlfriend's words or behavior can be analyzed without her being part of the conversation. Who knows why she said/did whatever the way she did? Only she does.

There is no "should" about length of time to move on. It is okay to remember and wonder about situations but not very helpful when you find yourself doing so; I would shift your focus when you find yourself wondering about past relationship(s) since you can only do things differently based on your own behaviors.

It's never "neat" when one person in a relationship finds/starts seeing another person; they don't know how to make the transition easy for themselves or the old partner. It's not like a job where you can turn in a letter giving two weeks notice, they throw you a party and wish you well, and off you go into your future life.

You miss her quirky little self; you were emotionally "invested" in her and it takes time to reclaim that part of you you gave her so you can move on; that's what grief/loss is. However you work on reclaiming, whether trying to figure her out or concentrating on other things in your life now or moving toward new things, it is all right, it is your way and there is no "best" way, just your way. I'm sorry she treated you this way, she does not sound very mature to me (and, given her age, is not all that experienced). But her words and behaviors are hers and in no way your fault! You couldn't have done anything differently and you'll never meet another woman like her; we're all individuals :-) From your description, it sounds like you did the best you could and I don't see anything I would have changed.

The only thing I, myself, would have done differently is not to have had a long-distance relationship or expected much to have come from one since the odds/percentage of time with the other person is not great enough to make them work very often, in my opinion.