I need help and although I could register on twitch affiliate but my mother does not want to give her tax ID because she thinks it is not safe.
You can't just enter your mother's tax ID there!
Do you need a trade
If your mother doesn't give the tax number, there are reasons.
You can do the affiliate program when you are 13, but you need the consent of your parents. This is also stated in the FAQ / in the contract.
In DE you need a trade, which is only possible from the age of 18.