What rules or lessons has Bud learned from the three families he was in?
I believe that this question is asking about the three families that Bud was with after his mother's death. Readers do get a flashback chapter in which we see Bud interacting with his mother and learning a lot of lessons, but I don't think that is the intent of this question.
The first family that Bud is a part of is the Amos family, and Bud doesn't really learn a whole lot of positive things. Todd Amos beats him up, lies to his mother about it, and gets Bud thrown into the shed. Bud gets his revenge, but I think his main lesson is that even people with seemingly good intentions can be quite nasty people. The Amos family made it sound like they were doing Bud a favor by getting him out of the orphanage, but it is clear to Bud and readers that they didn't really intend for him to be a part of the family.
The lesson that he learns from Lefty Lewis's family is quite different. Bud learns what a loving home can look like. The family takes him in, feeds him, clothes him, and Bud gets a vision of what life can be like with loving family support.
Bud finally obtains that once he joins the band in the final section of the book. The new lesson that he learns with the band is that to be a part of a functioning family, everybody has to work for it. The band definitely welcomes Bud to the group/family, but they make it clear that he isn't going to get a free ride. He has to contribute to the group wellness as much as any other person in the family.
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