The Question and Answer section for The Chocolate War is a great resource to ask questions, find answers, and discuss the novel.
I don't think there is any peace. There are dark undercurrents going on in the school. Archie invents ugly and cruel mental punishments - "assignments" - for various members of the student body.
Brother Leon is the head administrator at the school Jerry attends.
Jerry was thinking about his mother's death, which triggered his lunch to spill out, and he had pain too. That's what made him vomit was thinking about how his mother died.