Asalamu alaikum dear sister
of course child abuse is wrong, it's wrong to hurt humans whether theyre children, teens or adults.
Anyway, it seems like your mother is bringing out all her anger out on you because she's had a difficult marriage with you're father. At least they are not together anymore, so hopefully there wont be so much abuse.
Sister insha Allah I'll make du'a for you sis, this could be divine punishment from God for your sins. Maybe try being a better person and sinning less in general, then insha Allah you will have less worldyl punishment.
We all go through our own ups and downs in life, we all need the key called patience. Even though we still go through a lot of horrible things, we should still remember and be happy about the fun and enjoyable times in life as well.
You know those people in school that say you're so quiet and never talk and bla bla bla, just ignore them. So what if you dont talk a lot? I was the quiet girl in school as well yet I managed to make friends even though I didnt talk a lot. Insha Allah you'll make some friends, it takes time.
I know your Mum has been abusing you and hurting you and saying all these horrible things to you. BUT keep n mind that that's all just a reflection of her anger and her pain, she didnt mean to call you all those things, it just came out because she's angry and feels in pain because of how her life has been for her.
I know it's not right for her to physically or verbally abuse you but that is just a weakness on the part of your mum. My mom would also sometimes hurt me and hit me with wooden spoons and pull my hair like mad, but thats only because she herself eas in difficulty. So I dont go and run to and report her because at the end of the day she's my mother and i dont want her to get in trouble. After all, deep down I know that my mother has some good in her as well, otherwise why would she also be nice to me? I know your mother is also a nice person deep down inside her heart, so try and appreciate that (even when she hurts you)..Allah will reward you for your patience and for your forgiving nature towards your mum :)
And you know in tv they always do live appeals on Islamchannel and they said that if you give sadaqah (optional charity) it will be a means for which Allah will block calamity from your life.
So sis...my main advise would be to:
-make LOADS of Du'a to Allah
- be a better Muslim and sin less so that Allah will give you less worldy punishment
- give Sadaqah (charity) if you can, even if it's just even a pound, pop it in the Sadaqah box at your local mosque or something
and Im sorry that you're going through such rough times dear sister, may Allah shower you with his Mercy!
take care sis,
wassalam xX