CAMHS appointments take a very long time, speak to your dds school welfare teacher, they could give her 1-2-1 ELSA, See your GP frequently and make appointments with your GP for your dd. There are charities and agencies, she might be a bit young for Young Carers. Go to your local library and CAB and ask what is available locally.
For yourself contact Steps to Wellbeing and make a self referral.
Mostly it's taking the time to be a pita over getting help for your dd, this is what I've done for mine.
With the self harm I had a lot of success talking it through with her and said whenever she felt like harming, no matter what I was doing come and talk to me, I'll listen no matter what. She also had a Nokia brick phone to take to school so that she could call me during the day when I was at work.
This and schools Elsa appear to have got her past self harming, it was difficult but she's got through it.
For transparencies same I'm a lone parent single father to 2 DDS, my ex is no help, because of the reason behind me having full custody, I keep her at arms length because of issues, much like you describe with your ex. The court threats are often just those , threats used to grind you down. Until you get a summons, don't get worked up about it (I get those threat frequently, I now just ignore them).That and my parenting etc
Not having the money for a lawyer barrister is difficult, you offer get a free 30 mininute consultation with a lawyer, basically try before you buy, you could explain your financial circumstances and come up with a payment plan. Also you get to ask specific questions about what your ex is saying.
Don't fret, the courts only change the status quo if there is a really really compelling reasons to do so. If he's only had minimal contact over the last five years then he is in no position to suddenly change to 50% of his time looking after a child, he won't have the experience or understanding and that is not in the best interest of your dd. Especially if his lifestyle work means that he's working rather than caring. Few people have the understanding of how difficult it is to be a line parent with no extra support. Family court judges understand this very well and they are sympathetic.
It's horrible and scary what you are going through and I do have some understanding of the thoughts that will rock through your brain depending on what he's saying to you. Take each day as it comes, try hard to put the difficult thoughts he causes out of your head (it's not that easy I know) and focus on your own and your dd's well-being.