1) I have a question regarding offering namaz on burning coal to show the extent of their faith, it is a rare practice done by Shias in Pakistan and India.

Is it permissible? If yes how can we justify it?

2) Qama Zani to an extreme level when the back opens into two parts, is it permissible?

1- It is not permissible.
2- It is not permissible to seriously harm the body, and it is not part of the religion.