You are not responsible for what's ailing your daughter. Self-mutilation can have a host of underlying factors - the only person who knows is the victim. A good counselor/therapist will help your daughter explore different coping mechanisms, but the therapy may take a long, long while. Please, understand that in order to help your daughter, you cannot accept blame, guilt, or responsibility for her actions. Your strength and courage will be a support for her through the difficult healing processes that she's facing.
Demanding that she disclose the details of her rape, near-rape, almost-molestation, etc., will only widen a chasm - let her know that your "emotional door" is always open and that you will not stand in judgment, regardless of the circumstances - she will begin speaking if and when she is ready. Most rape victims feel as if they could have avoided the act of violence that was perpetrated against them, "If only I hadn't _____ (had alcohol; walked on another street; left the house 5 minutes sooner; etc.), this never would have happened." For some, it takes years to be able to speak about what happened. You SHOULD feel righteous anger that the parents of your daughter's friend kept silent! They may not be directly involved, but they were responsible for her safety while she was in their home and they chose to keep silent about a criminal, violent act against her. No doubt, they were afraid of the implications of what their "guest" did, legally and morally. And, shame on them!
That your daughter is of legal age could make things difficult for her recovery, so be prepared. She is legally able to walk out of therapy and you cannot force her to engage in anything that she doesn't want to participate in. Of course, pressuring her to remain engaged in therapy could also backfire. You may not even be legally allowed to speak to her therapist - patient rights have changed dramatically over the past few years, and even conscientious parents have little-to-no access to their adult children's medical/mental health providers. It might be prudent to seek your own family counselor/therapist to help you to help your daughter.
God bless you and best wishes to you and your family.