Eating disorders are very insidious and very, very hard to break. It make take several attempts at treatment for your friend before she starts to get better. I'm very glad she's getting the help she needs, though. And I'm also very glad you've been such a good friend to her. It really sucks to try and help as much as you can and watch them get worse, doesn't it?

As for the bingeing, that is a subtype of anorexia. They do purge, but not in the usual way of vomiting - they can purge through compulsive exercise, too. It's not all that unusual, actually. A lot of us picture anorexia as constant never ending starvation, but they can and do binge - usually for them, food is a control issue and signifies that there's something much deeper going on. Therefore, food and everything related to it has significant emotional connections. Bingers usually eat in response to some sort of stressor - feeling down, feeling up, feeling lonely, etc. For an anorexic that can be sheer hell because she feels like twice the failure for losing control.

I hope your friend starts to heal - it will take time but don't forget her simply because you don't see her at school. People with depression or any mental disorder need friends so badly right now, even if they try to push you away. Change and taking that first step towards healing is monumentally terrifying, even if its for the best. Don't fail to remind her that first and foremost, she is your friend and you'll always be there for her. It's frustrating, yes, but it will be so much harder for her to do this alone.

some of it's magic
some of it's tragic
but i had a good life all the way......
~jimmy buffett