Always, I have been here with dd so my heart is breaking for you. I can give some advice based on what I have done with dd.
Skinpicking is s form of self-harm, just subtle. My dd also bites nails until they bleed, scratches body during meltdown or anxiety attacks and this has escalated to using a scalpel/razor on her arms. She is 14 though. A hair band on the wrist like @sirzy has and encouragement to ping it when needed is helpful.
Regarding the anxiety, it has reached crisis level so please keep calling camhs, sob down the phone until they offer help.
And in terms of how to help DS, firstly just take a step back. Stop, get some sleep yourself and leave him be if you think he is safe. He will feed on your stress and exhaustion. When you have had some rest and can deal with this a little better then try and prioritise what you are trying to achieve. I would suggest:
Don't worry about him not leaving his room for now, take whatever food and drink he considers acceptable to him just so you know he is eating. A brain without supplies will not work properly. We learnt this through DDs ARFID.
Don't force any interactions on DS. My DD still struggles with DH. They haven't touched for 2 years except maybe 5 hugs at dds instigation.
Just think of today. Get through today. Talk to DS about what he would like to do, focus on positive reinforcement all the time (not easy) and you may spend the day in his room. But try and spend the day doing something other than focusing on sleep or getting him out if at all possible. 1leap is correct that a standard wake time needs to be brought in and the sleep will take a while to fix, my dd literally cannot sleep without melatonin though. Ask the gp for a paediatrician referral.
Keep posting here. The gang have helped me many times...