I don't know what kind of doors you have that your chinchillas can open, but... That could be a very big problem for you. Even if my chinchillas could reach the door knobs with a jump, they couldn't twist it to open it and they certainly couldn't pull it when it weighs SO much more than they do...
Unfortunately, some chinchillas are biters. It doesn't necessarily have anything to do with having a bad experience. (Which isn't to say that your chin hasn't experienced something bad... I'm just saying it isn't necessarily fact.) In the 5+ years I've been breeding chinchillas, I've had ONE chinchilla born here who just thought that biting was one of the best things ever. He wasn't nearly as aggressive as your girl and didn't bite me every chance he got, but he would bite when the mood struck him. The trick was to find out how to get him to stop. In his case, he liked it when I blew in his face, so that didn't work. Saying "NO!" loudly and firmly didn't phase him, as I was pulling my hand away and essentially giving him what he wanted. I had to wear thick gloves and let him bite without pulling away while saying, "NO!" loudly and firmly... And this started to work. This may be something that you can try with your girl.
I would suggest finding a way to prevent her from getting out of the cage until YOU are ready for her to be out, which I wouldn't recommend doing until you've bonded with her more and she isn't biting you whenever you reach into her cage. This will take time and a LOT of patience on your part... It may end up being a battle that you never win, unfortunately. Not all animals can be "tamed."