The school is probably exessive in their disipline, but it is a life lesson he must learn. It is important that his teacher not treat him like a criminal when he returns to school. He is five, and I am sure he will not play with lighters anymore.
I realize the pretend campfire was probably what gave them the idea, but he is still responsible for his actions. This situation can be made positive by showing him how our actions have certain outcomes. He is not a bad person, he just didn't follow the rules.
I read an article once that when a child completes their punishment, the family will celebrate with going to ice cream or some other treat. That way the child realizes they are not bad, and they have done their "time."
About the girl, that is sticky. Since he can't control the girl, he can only control what he does. Another life lesson that he may be too young for, but it is worth a try.
About the public school thing, are the teachers meaner to him than other kids because he may be challenging? Since he is five, you could pull him out and have him return to school later. He may need more time at home, boys don't develop socially as fast as girls.
There are books out there about the "spirited child" and how to raise them. I like that term because it stays in the postive. Also if he is really bright, public school will be boring for him.