I am sorry that you are going through all of this. It is a difficult history to cope with, both for survivors and for people who care about them.
If you are interested, you will find many relevant threads on this particular forum. I encourage you to read as much as you can tolerate at any one go. The information and the disclosures are often very painful to read--even though there are some threads with positive and encouraging reports. Unfortunately, the balance is much more toward the side of struggle than the side of triumph. It is a challenging, very long-term project, this task of recovery.
I speak from my own experience as the partner (first girlfriend, then housemate, now fiancee) of a CSA survivor. Whatever I say please take as being my own opinion, not anything "authoritative."
I remember in the early days of disclosure, when my F and I were about 18 months into the relationship, feeling honored and flattered that he trusted me as much as he did to confide in me about his abuse.
Today, after many more years of real-life interactions, my understanding of that is much more complex. It's an honor, perhaps, but in some ways also a burden. It appealed to what I now see as my "rescuer" tendencies--traits in my character which are not solely positive.
I suspect this is why so many people replying to you are saying:
--make sure you take care of you first
--make sure you take care of your daughter first
--make sure you are aware of how complicated this can get.
I am going to sound cynical if not bitter, but from what I have experienced (and read here), I would guess that there is a lot more to the story that you do not yet know, and that you may never know.
You must protect yourself. If your BF is having sex (unprotected or not) with anyone else, then he may pick up STIs, including HIV. It is imperative that he and you be tested.
I also recommend that you investigate S-Anon, the 12-step program for people affected by their relationships with someone who has a sexual addiction. It has been a lifeline to me. Whether you are ready to apply that label to your BF or not, there is no harm in checking things out there for yourself and seeing whether it has relevance for your life.
Good luck to you, your daughter and your BF.
I'm just a poor wayfaring stranger, a million miles away from home.