In The Boy in the Striped Pajamas by John Boyne, what did Bruno think Herr Roller should do, and why?

First, it is important to realize that Herr Roller is more often called Franz within The Boy in the Striped Pajamas.  (This should clear up any character confusion.)  In answer to your question, we learn about Bruno’s thoughts in Chapter 7, when he is speaking to his mother.  In short, Bruno thinks Herr Roller should neither have arguments with his shadow nor allow cats to come to tea parties.  Bruno does not consider these behaviors “normal” and continues to laugh at Herr Roller.  Bruno’s mom reprimands Bruno for this vitriolic laughter.  She tells Bruno not to laugh because Herr Roller suffered a lot due to World War I.  “You have no idea what the young men went through back then. Their suffering.”  This statement is a perfect example of a particular kind of irony:  dramatic irony.  Dramatic irony exists when a character does not know something that the reader knows.  In this case, the irony will become clear as the reader observes the suffering of the Jewish people at the hands of the Nazis.