Bruno's relationship with his mother can reasonably be described as difficult. This is largely because, in the family dynamic, she is on the side of her husband, acting as his loyal lieutenant when it comes to instilling the children with discipline and Nazi ideology. That's not to say she isn't a loving mother to Bruno. It's just that the normal mother/son relationship has been complicated and distorted, like everything else, by Ralf's new post as Commandant of Auschwitz.

Though very naive about the war and about the horrors of the concentration camps, Bruno is still an inquisitive young boy and wants to find out more about his surroundings. However, his mother expressly refuses to discuss anything that might compromise Bruno's innocence. In all probability, she thinks she's doing the right thing by protecting her son from the harsh realities of the world in which they live. However, Bruno's too young to understand this and resents his mother's stern refusal to answer difficult questions.

What is the relationship between Bruno and Shmuel in The Boy in the Striped Pajamas?

Bruno and Shmuel, both characters in the poignant novel The Boy in the Striped Pajamas, become best friends, despite their backgrounds and realities being worlds apart.

Bruno is the son of a Nazi officer who works at the Auschwitz concentration camp and has close ties with Germany's dictator, who Bruno calls "The Fury." Shmuel is Jewish, and is a prisoner in Auschwitz. Bruno has lived a sheltered life, which is the cause of his naivete, while Shmuel has been denied basic human rights, imprisoned, robbed, and exposed to untold horrors.

The friendship is a surprising one in many ways, with Bruno having been indoctrinated to think that "Germany is the greatest of all countries," and Shmuel being a Polish Jew. It also stands to reason that Shmuel, as someone imprisoned due to the beliefs of Germany's dictator, could have been skeptical about befriending a German boy.

When Bruno and his family first arrive at "Out-With," Bruno is devastated to have had to leave his close friends, Karl, Daniel, and Martin, behind in Berlin. His friendship with Shmuel, which soon evolves to be deeper than any of those he had back in Berlin, becomes a central focus in Bruno's life. Friendships and having someone to play with are extremely important to Bruno.

While Bruno redeems himself at the end of the novel, he is not always a good friend to Shmuel. When Shmuel is brought to Bruno's home as a servant, he begs Bruno for some food, which Bruno gives him. However, when a Nazi officer catches Shmuel eating, he accuses Shmuel of stealing the food, and Bruno's failure to defend his friend earns Shmuel a beating.

When Bruno's mother hatches a plan to move back to Berlin with the children, having realized that a house next door to a death camp is no place to raise children, Bruno is once again devastated at the thought of leaving a friend behind. In the ultimate display of loyalty to his friend, Bruno climbs under the fence and dresses in the titular "striped pajamas" to help Shmuel find his father, who has gone missing. The book has a tragic ending when the friends are inadvertently swept up in a march to the gas chambers. By this point, Shmuel is the closest friend that Bruno has ever had. This friendship has caused his former friendships with Karl, Daniel, and Martin to fade into such insignificance that he can no longer remember their names or what they looked like.

In The Boy in the Striped Pajamas, what is the relationship between Maria and Father?

In The Boy in the Striped Pajamas, Bruno's father is a Nazi commandant. The family has to relocate to "Out-With" as Bruno's father has been appointed there. Maria, the cook and the butler have all gone with the family and Bruno tries to talk to Maria about how "desolate" the new house his. Bruno is unimpressed that they left his beloved home in Berlin, and in chapter 6 he is convinced Maria, as part of the "family" must feel the same way.

Bruno even suggests that his father is "stupid" to which Maria reacts, explaining that his father is "a very good man." She tells Bruno that her own mother knew Bruno's father when he was a small boy because Maria's mother worked for Bruno's grandmother as a dressmaker. Bruno listens attentively as  Maria continues to explain about her relationship with Bruno's father. She tells him that Maria's mother remained friends with Bruno's grandmother after retirement and also received a small pension and when Maria's family were in dire straits, Bruno's father gave Maria a job. He also paid for Maria's mother's medical bills when she got sick and so he will always hold a special place in Maria's heart. She mentions the "kindness in his heart" and she trails off when she ponders what he is a part of now. 

What is the relationship between Maria and Pavel in The Boy in the Striped Pajamas?

Pavel and Maria are both servants in the household of Bruno's family; Maria travels with them from their original home, while Pavel is assigned to them from the concentration camp. Pavel used to be a doctor, but was stripped of his social status and wealth when the Nazis invaded, and sent to work alongside other Jews in the camp. He now works as a waiter and does not speak of his former stature. Maria is a maid and is friendly with Bruno; while he is of a higher social class, he treats her -- and Pavel -- with childlike deference, as they are adults. Maria is able to translate some of the adult ideas that Bruno experiences into ideas that he can understand, as when they discuss Pavel:

"He said he was a doctor," said Bruno. "Which didn't seem right at all. He's not a doctor, is he?"

"No," said Maria, shaking her head. "No, he's not a doctor.

[...]

"But he was. In another life. Before he came here."

Bruno frowned and thought about it. "I don't understand," he said.

"Few of us do," said Maria.
(Boyne, The Boy in the Striped Pyjamas, Google Books)

Pavel and Maria do not share any major scenes, but it is indicated that Maria understands how Pavel is unjustly punished for the crime of being Jewish. Maria is also the one who cleans up after Pavel is beaten to death by Lt. Kotler; she is unable to save him, but she saves Bruno from the emotional pain of seeing Pavel dead and bleeding. The connection between them is mainly of the working class, with Maria accepted as a normal part of society and Pavel indicted as a slave for his heritage.

What is the relationship between Bruno, Gretel, father and mother in The Boy in the Striped Pajamas?

The most evident answer is that the relationship between all four characters is that they are a family, the central family, in Boyne's novel.  They are all linked by blood and the relationship they share.  As a family of four, they are the center of the narrative.  On a more symbolic, the German family might be seen to represent the different aspects of German society during the Holocaust.  Father is a believer in Nazism, representing the significant part of German society that embraced Hitler's ideology and what it meant.  Gretel is one who becomes infatuated with the power that accompanies Nazism, not fully aware of its implications.  The mother of the family struggles between the support of her husband and the need to shelter her family from what she knows is wrong.  Bruno could come to represent the portion of German society that stood up to the Nazis.  While not significant in mass numbers, there were Germans, good Germans, who recognized what Hitler was doing as wrong and stood up, paying the ultimate sacrifice, because of it.  I think that this might be where the relationship between the family members can come to represent more than the central characters in the Boyne novel.