Three weeks isn't really that long of a time period man. I know you are afraid to lose things completely with her, and you rather have her as a friend then nothing at all. The thing about being friends is that you can strike it up anytime YOU want to. Relationships, not so much. And if you want more than friends, don't settle for anything less. Because she WILL have another guy, and then all the sudden you will be hurt, pissed off, and not want to be friends because it hurts so much. And you will have nobody to blame but yourself because you put yourself in that situation.
So she wanted to break up. She did this for a reason, she wasn't happy, and this is what she wanted. The kind of behavior she is exhibiting is actually in her own self interest. Isn't it sneaky when they disguise it as "how are you doing?" and all that? In a way, I'm sure they care about you and how you are doing, but they ultimately are making sure that you are still around for them. That you still care about them, that if they wanted to, they could just come back to you and you would be there for their everything. That you can't live without them and NEED them in your life. It's to feed their ego, which is always in tatters after a serious relationship. So if you want to give yourself a little satisfaction, don't feed their ego.
This is ultimately about you and what is in your best interest. Until they come to you and say, "I want you in my life", assume they don't. And if they don't want you in their life, what does it matter how much you want them to be? You need two to tango man. The best thing for you would be to be on your own without any of their interference until you are okay and do not feel the need for her to be in your life. Because once that happens, you will be ready for somebody that does want you in their life for the right reasons and able to give you their 110 percent, which your ex cannot. You shouldn't need them in your life, you should want them to be. Big difference. When you think that maybe you could work things out, you have to remind yourself that it logically can't work. You guys are who you are now, and you broke up. Have you both really changed much since you broke up, and will in a couple weeks? No. And you both would need to change to be different people in order to have a chance of it working out.
Bottom line is to focus more so on yourself and having fun, living life without her. Not on when to talk to her and when to try to get her back. If she is trying to talk to her, just remind her that this is what she wanted and you aren't ready to be friends. You can do it nicely and politely. Trust me, it's in y our best interest to do so. It takes some time, so don't count the weeks. You will never make it and cave on her.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.