Hi Flash76 and welcome to the forums.
Wow, what a challenging situation your friend and her daughter are in! Self-harming is a very difficult situation for those who are engaged in these behaviours and those caring for them. It can be very challenging to see someone in such distress, particularly when there is anger and blame involved.
H may find seeing a psychologist one on one to be quite confronting face to face. There are multiple options for other supports including Kids Helpline (1800 55 1800 or https://kidshelpline.com.au/get-help/webchat-counselling), headspace and these beyond blue forums. I have found that children and adolescents find it easier to engage on a text based platform like the one suggested as there is a degree of safety and less vulnerability in doing so.
It's important too that E seek professional support. There are many carer support groups out there, including Mind Australia (https://www.mindaustralia.org.au/ or 1300 554 660). You need not feel, despite how close you are, that you must be responsible for ensuring E and H receive the appropriate support. The best thing that you can do as a friend is to be a guide to point them in the right direction.
I hope things improve for all of you.