How does the novel deal with the theme of fear? Is fear important in the lives of Anne and other characters? How do they deal with it? Choose three characters as part of your analysis with specific examples from the novel.

The Diary of a Young Girl is told from the perspective of Anne Frank, a Dutch girl who went into hiding with her Jewish family (and a handful of other people) during the Nazi occupation of the Netherlands.
During two years of hiding in the annex, several events occur that incite fear and anxiety in the characters. It is important to note that we, as readers, learn about that fear only through Anne's descriptions: we cannot know how other characters experienced the same events. Everything is filtered through Anne, and she has closer and more sympathetic relationships with some characters (like her father, and, later in the diary, Peter) than she does with others (like her mother, which whom she does not have much in common.)
Let us look at some examples of terrifying events in the text and how three characters (Anne, her father, Otto, Peter, and Mr. van Daan) react to them:

MONDAY, JULY 26, 1943A big fire like that is not a pleasant sight, but fortunately for us it was all over, and we went back to our various chores. Just as we were starting dinner: another air-raid alarm. The food was good, but I lost my appetite the moment I heard the siren. Nothing happened, however, and forty-five minutes later the all clear was sounded. After the dishes had been washed: another air-raid warning, gunfire and swarms of planes. "Oh, gosh, twice in one day," we thought, "that's twice in one day," we thought, "that's twice too many." Little good that did us, because once again the bombs rained down, this time on the others of the city. According to British reports, Schiphol Airport was bombed. The planes dived and climbed, the air was abuzz with the drone of engines. It was very scary, and the whole time I kept thinking, "Here it comes, this is it."I can assure you that when I went to bed at nine, my legs were still shaking. At the stroke of midnight I woke up again: more planes! Dussel was undressing, but I took no notice and leapt up, wide awake, at the sound of the first shot.

During this air raid, Anne is quite scared, and she is very clear about it. Her fear manifests itself emotionally and physically (as she writes, her legs were still shaking a while after the air raid was over.)
How does her father, Otto, react to the same event?

I stayed in Father's bed until one, in my own bed until one-thirty, and was back in Father's bed at two. But the planes kept on coming. At last they stopped firing and I was able to go back "home" again. I finally fell asleep at half past two.

Anne makes no mention of her father's experience of fear. As in various other points in the diaries, he is trying to protect Anne and take care of her. The fact that she omits any mention of his own anxiety confirms this: in the face of fear, Otto plays a reassuring parental role. 
In addition to the air raids, break-ins downstairs at the business beneath the annex also cause fear and worry among the small group that is hiding upstairs. They are afraid that their presence could be detected by burglars or that police could come to the scene of a burglary and discover the people hiding in the annex. Anne describes one of these incidents here:

TUESDAY, APRIL 11, 1944
Peter was on the landing when he heard two loud bangs. He went downstairs and saw that a large panel was missing from the left half of the warehouse door. He dashed upstairs, alerted the "Home Guard," and the four of them went downstairs. When they entered the warehouse, the burglars were going about their business. Without thinking, Mr. van Daan yelled "Police!" Hurried footsteps outside; the burglars had fled. The board was put back in the door so the police wouldn't notice the gap, but then a swift kick from outside sent it flying to the floor. The men were amazed at the burglars' audacity. Both Peter and Mr. van Daan felt a murderous rage come over them. Mr. van Daan slammed an ax against the floor, and all was quiet again. 

How do Peter and Mr. van Daan react to fear in this situation? They are both proactive, and they try to defend the safety of the group. True, Mr. van Daan yelled "without thinking," but it is not like he is upstairs in the annex, hiding under the covers. He, like Peter, is filled with adrenaline; as Anne puts it, he is filled with a "murderous rage" that motivates them to resolve the frightening situation with the burglars as definitively as possible.