What sort of eating disorder does she have, and how can I help her?

It sounds like she has bulimia since shes throwing up or even body dismorphic disorder.Also just because she's in a healthy weight range doesn't mean she doesn't have an eating disorders.Fat people can have anorexia,bulimia,ED-NOS as well as skinny people.I suggest you tell her family before this gets out of hand there is help for these type of eating disorders.She may not like you for it,but in the end she will see why you did it.