In the film version of The Power of One, why won't Maria's father allow her to date Peekay?
We are limited to answering one question at a time; so I edited your questions to one.
In South Africa during The Power of One's time setting, the country was not only divided by race but also by the national origins of South Africans. Maria and her father are Afrikaners (Africans who descended from the Dutch and German colonists), and Peekay is of British descent. When Peekay asks to date Maria, World War II has just ended--a war which pitted Peekay's "people" against Maria's. Moreover, when the British ruled South Africa, they forced many Afrikaners into concentration camps, understandably resulting in long-term resentment from the Afrikaners.
Not only is Peekay facing Maria's father's natural prejudice toward him when he asks to date her, but the young man is also opposed to many of Maria's father's political initiatives like apartheid and is unafraid to say so.