My daughter suffers from annorexia, but lately has been doing a lot of strange late at night binges?

The best advice and help you can get is from the therapist that she is seeing. This is dangerous and just as dangerous as not eating. You can go to the site nami.org which is the site for the National Alliance on Mental Illness. On their site you can find the phone number for your local chapter. They are there for support, information, and they have the best resources for the help that your daughter needs in your area. It would help to talk to them if her therapist isn't helping her.