Saul sees the school as a constant force on the students. What does he see as the only way to stop the harm being done to the students? Also, how does Saul manage to survive the school and come away alive?

What chapter are you referring to? I don't recall what Saul thought could stoop the abuse. The only thing that enabled Saul to escape the school was his hockey talent and his relationship with Father Leboutilier. Ironically it is both these things that almost destroy Saul in the end.