Welcome to the forum and I am so sorry that you are going through this with your daughter, and her friends too. I am a mum and I can imagine the worry and the stress that this is causing for you and your family in how to help your daughter.
I would also like to say how wonderfully you are doing with communicating with your daughter and being able to talk to her about what is going on with her friends and how to support them and also what is going on for her. I am sure that your daughter is going through all sorts of emotions and especially if her friend is expressing to her that they are self harming or having thoughts of suicide. I can see Sophie_M has given you some numbers and I would like to echo the support of the Kids Helpline, they are so wonderful and would be able to provide some wonderful support, to both you are your daughter through this. The Kids Helpline number is 1800 55 1800 but they also have a service that is web based should your daughter feel more comfortable in typing rather than talking:
I understand where you are coming from in wondering if your daughter has taken to harming herself "because her friends are", however with this type of behavior all seriousness should be given to it. She may very well just be curious and wonder what it is about and how it feels, she also may not and I am so pleased you have the support of the school and also an appointment with a professional.
As you seem to have such a great line of communication with her do you feel like you could talk to her about her harming herself and ask her softly about how she was feeling when this happened? Even just listening to her express her feelings without the need to "fix" it might really help her too.
It also seems she is feeling alot of pressure to "fix" her friends and I think by her getting some support she can manage how to navigate the conversations with her friends as well as know when it is ok to step back and that it is not her role to "fix", but to just listen and to love and support, I am sure you have said that to her already.
I am so pleased you have reached out today and have come to chat and to get some support for yourself, that is so important too. We are here for you.
Huge hugs to you