Dude, you are absolutely INSANE! For some unknown reason you point out she's been abused in the past, yet you sound like the type that would progress into abusing their SO. If not physically, definitely verbally because you are already there. Implementing rules, not allowing her to speak to others a few weeks into a relationship, you make me sick. You sound like those dudes they show on daytime talk shows that think they literally own their wives/girlfriends. How old are you?
I'm going to go out on a limb and say you've never been in a real relationship, or at least a stable one. You can't start a relationship off by telling her that you have serious trust issues and that she needs to prove right away that you can trust her. I've got trust issues...you don't have issues, you're beyond that, you need to see a mental health professional. In addition, how in three weeks are you already "in love?" You've both got serious problems. I assure you, you are not in love. I'm not saying you won't be, but nobody is really "in love" 3 weeks after meeting each other. Breaking this thing off shouldn't be an issue for her if she wants to, that just once again is an attribute of her incredibly diminished level of maturity. Breaking up with someone after 3 weeks should be no sweat off anyone's back. We've all been there many times. Unless you're incredibly sensitive, that's the time where a breakup occurs and you'd think, "hopefully I'll have some better luck next time." You shouldn't even be in a relationship until you're comfortable enough with yourself that you won't act like a crazed lunatic.
BROKEN HEARTS ARE FOR ASSHOLES.