Oh OP. My biological mother was the same - so much is similar .
There is some very wise advice here from people who understand all too well.
My two cents' worth: Your mother was extremely damaged (do you know any of her own childhood) and when that happens, especially young, someone can grow up trying to look after themselves and protect themselves but without any idea how to do it properly. So instead of setting reasonable limits (how can a 7yo child set any limits against an abusive parent? they can't!) they try to take care of themselves by looking after their feelings. They are fighting a huge battle between their own tempestuous emotions and need to be valued, and their more sensible selves that know that 'something is very wrong'.
Over time the need to protect their own feelings and self-worth becomes greater and greater and the more sensible part is slowly worn down and destroyed. So they become ... honestly, monstrous. Full of pain, and passing that pain on to others. People with severe untreated BPD are catastrophic parents because inside, they are still (or go back to being) toddlers but with an adult's body and powers. No one wants to be at the mercy of a toddler.
As they get worse, their perception of reality changes and decays until everything that happens, happens only in relation to them. They are the sun and everyone else orbits around them and must serve their needs (usually guessing what exactly is needed without being told and woe befall you if you don't understand without being told).
The only way someone with severe BPD can be helped is if 1) they want help and 2) get the right support - DBT treatment and people around them who can be supportive but also put up very firm boundaries. I've seen it work.
Without that will and without the right support and people around them the result is ... your mother, my biological mother and the parent of some of the other people on this thread. A destructive wreck living in great pain/distress and spreading great pain/distress. She may have loved you in her own way (the presents) but her absolute inability, and it probably was inability, to control her pain dominated her life and yours then. The bonds we have with our mother run deepest of all, I sometimes think, maybe second only to the bond with our own children. Certainly broken/destructive bonds with our mother affect many of us all our lives, although some healing can come.
There was nothing you could have done as a child. Nothing. As I say I've seen it at close quarters and seen the effects on the children involved too, and it's heartbreaking.
Which leaves you with a complex problem - you love her, you want her as a good mother. It's the puppies who are given the most love, attention and healthy boundaries who grow up the most confident and happy dogs. The ones who are loved one minute and pushed away or punished the next don't. We aren't much different, tbh.
Someone up thread used the words 'witch' and 'waif' and they fit very well for the woman you've described. Neither can be a good mother. I really think you need therapy, and probably a lot of it with the right person, before you can begin to make sense of your experience of your mother and give it a place in your life. Otherwise it's at risk of influencing you in ways that you may not even realise, as is happening in my biological mother's family with her children.
What I would say, gently, is that people are capable far more extreme behaviour than we ever like to think. Your mother is not unique; nor are the other sorts of appalling parents. The explanation for yoru mother's way of existing may lie there. It's said with BPD that 'genetics loads the gun, environment fires the trigger'. Something almost certainly happened to your mum in her childhood that was bad enough that it tipped her off balance and without treatment she spiralled off worse and worse. I'm afraid that sometimes people can behave like she did, or become as ill as she was, or sometime simply choose to behave in ways that can only be called wicked.
I hope that one day you can find a measure of peace, OP. Sincerely wish you well, and I'm so very sorry for the pain and confusion and hurt you went through as a child. You ~can~ give it a place in your life-experience but I do think you will need help.
(and if you managed to read all that, wow heh)