There are several questions being asked here, so I will limit this answer to the climax question as it allows for a more objective answer than the following questions. The climax of the novel begins after Bruno decides to dress up in the concentration camp "pajamas." The reason that he is going to dress up like that is to be able to pass as a prisoner on Shmuel's side of the fence. The two boys plan to look for Shmuel's father. More than likely, readers know that their plan is likely to end badly, but we do not quite know how it is going to end. The tension at this point is ratcheting up very quickly.
The boys do not find Shmuel's father, and Bruno decides it is time to head back to his side of the fence. Unfortunately, they are surrounded by soldiers and forced to enter the gas chamber. The two boys hold hands, and the lights go out. Chaos follows, and readers know that neither boy is going to survive. From this point, the novel moves from the climax into the falling action and resolution. The novel turns to Bruno's family, and they are struggling with his disappearance. Gretel and mom eventually return to Berlin. Bruno's father finally figures out what happened to his son, and he is horrified. The novel ends with Allied soldiers arriving at the camp.