What courtesies did the teacher ask the students to observe? Why did he ask them to observe these courtesies?

Braithwaite (in the film his name is Thackeray) sees a major problem in the way his students interact with him and with each other. They show little respect, and also are behind in what he has expected their academic skills to be.
He believes a first step is to effect a change in their manners, by having the boys address the girls as "Miss," for example, and the girls to address the boys by their surnames, as Braithwaite himself does. Braithwaite is at best surprised and at worst appalled by the street language used in class by his students, and is successful, ultimately, in having them clean it up. He sees these apparently superficial measures as a means of facilitating the students' learning of the academic subjects, and it turns out that his insight is greater than that of most of the other teachers.
Though the discipline problems he has seem mild by our present-day standards, two things must be kept in mind. First, the novel was written nearly 60 years ago. Second, conditions even in a working-class part of London at that time were somewhat different from those in similar areas of the urban U.S. of the same period. To Sir, with Love is a relatively gentle and optimistic novel compared with what is probably the best-known American school story of that general period, Evan Hunter's The Blackboard Jungle. You might wish to take a look at it as well and ask whether this novel, or To Sir, with Love, is more realistic or relevant to the ongoing issues encountered in school.