"Informal and questioning" is a very interesting way to describe the tone in The Boy in the Striped Pajamas. Yes, this choice of wording in regards to the tone of the novel can be proved through quotations and examples. Let us take each part of your description in turn.
In regards to the tone being informal, the reader has to remember that the speaker and narrator is an eight-year-old boy, Bruno. A child of this age will almost always use an informal tone when speaking. The most famous example of this from the book is Bruno's misunderstanding of certain words. Most importantly, Bruno thinks the concentration camp Auschwitz is called "Out-With" and Hitler (or "the Führer") is called "the Fury."
In regards to the tone being "questioning," this can be proved as well. Bruno is very inquisitive and curious. We first find Bruno wondering why "the Fury" has to be invited to dinner. Next, Bruno wonders why the family has to move away from their home in Berlin. Later, Bruno wonders why the people across from his new house are all dressed in "striped pajamas." Further on, Bruno gets even more interested, so he decided to walk the length of the fence. In this way, Bruno meets Shmuel and creates a deep friendship in the midst of the Holocaust. Even when Bruno enters the gas chamber with Shmuel, Bruno does not really understand what is happening. He only knows that he needs to hold Shmuel's hand and to not let go because they are "friends for life."