Still have feelings and can't get my ex-girlfriend out of my mind, what to do?

My ex girlfriend broke up with me about 3 month ago after being together for about 8 months. After the breakup she told me she still loves me and wanted us to be friends but wanted to be able to hangout with other people. About a week after the breakup I saw her together with her old boyfriend how lives in another country. We went out for dinner a couple of times, at this point the old boyfriend had left, where she touched me a lot, kissed, and we ended up having sex. The last time we went out for dinner she was going to sleep at my place, we would have had sex again but she got her period. We started to talk about our issues as a result she went home, said she had to protect herself? About 3 weeks ago I got a email from my ex (after about a month of NC, we have never communicated though email before) with subj "Help". She asked me not to tell her old boyfriend that we had sex after he had gone back home if he contacted me and that her life was falling apart. I replied that I would/will never hurt her. She then replied "Thanks, that means a lot..". Later got a text (this time on WhatsApp?) where she said her old boyfriend was hurt and wanted me to know that he knows we had sex.

Send a couple of texts to her about 2 week ago, got 8 very angry text back telling me to stop contacting her. Says she wants to spend the rest of her life with her ex and she is trying to make things right with her ex. Even got a email which I wasn't suppose to answer, explained that we where never together and only had oralsex. Later got a message from her ex boyfriend how she is visiting asking about the relationship status between me and me ex girlfriend. Sent HER a reply explaining why I sent the messages, got a positive reply "I know your only mean well". Haven't been in contact since that but want her to know that I can't be just friends, don't know how to let her know or if it even matters. Want her back but I know I have to let her go, don't know how.

What a messed up situation. All I have to say is, **** that noise. Cut her out of your life. This is so much unnecessary drama.

Why would you even want her back, she basically just wants to sleep with both of you, and is deceitful, as you can see how she is behaving with the other guy.

"She asked me not to tell her old boyfriend that we had sex after he had gone back home if he contacted me and that her life was falling apart. I replied that I would/will never hurt her" So you're encouraging her deceitful and bad behavior, I think you're making yourself out to be a pushover.

This is what I would do, if I wanted her back, which I wouldnt. But I get it, you have all these attachments to her already which makes it hard to break away.

I would say,

-Hey, I want you, but i want nothing to do with this situation. It's just unnecessary drama, and my life is a drama free zone. Im moving on. Let me know if it doesn't work out with him, and if I'm still single, maybe then we could see where things go with us. Cheers.

Then. No contact unless she messages you. And no contact means no contact. If she doesn't reach out to you, you two will never communicate again.
If she reaches out, ask her out.

Yes it was/is a bit of a mess, and she is fully aware that she messed things up. She has different tones when texting (harsher) and communication on email (softer), might be me overanalysing. Me becoming a bit of a pushover was one of the reasons of the breakup. One of her best and oldest gf how I know as well, how happens to be together with my brother, initially felt like the two of us might get back together after a month or so after the breakup. After our last communication when she got really pissed my ex called her gf how send me a text telling me that my ex doesn't want me to contact her anymore and that she will never comeback. My ex and her friends have told me that her old bf treated her really bad, but she still went back to him. Like you mention not going to be the one initiating contact and if she does, which I after all do want, I will say something similar to what you say.