She's 13 and she needs help.
I wouldn't say it's a case of keeping her secrets or not it's more of a case of how to help her.
The one that concerns me the most is her older friend and her boyfriend displaying sexual activity in front of her.
Your definition of my definition of sexual activity might be quite different, so it's hard to say how far you need to take this, how did she seem to feel about it? If she was uncomfortable about it, you need to help her find a way to tell her friend that it's not acceptable to behave like that in front of others. Is she in a situation when she's with them that she could ring her dad or you or Mum to be collected? I wouldn't personally tell either of her parents, but I would make sure myself that the situation Was under control
As for the shoplifting what was her attitude like about that? Does she want some intervention to stop the Friend doing it? Does she just want to make sure she doesn't get caught up in it or did she think it was kind of cool. It's another thing it's not at the stage. I feel you need to tell the parents but you do need to make sure that what she wants to do about it. Is a acceptable and B she has a way of doing it.
With regard to her lack of self-confidence, I would just boost self-confidence and see if you can find a way that her dad can boost self-confidence without being obvious about it and maybe tell him she's struggling a bit with self-confidence but don't tell him that that's why she's not going to the party
Unless the stuff with her mum puts her in any kind of danger, I wouldn't say a thing young teenagers are often not very nice about their parents. I definitely wouldn't encourage it and I talk to her about what she says if there's an appropriate conversation you can have about it but other than that in one ear and out the other nothing that needs to go to the parents.
That way, you should be able to help her without breaking her confidence