Why did Twain choose the reign of Edward VI about which to write his novel?
Edward VI was the only male heir, son of Henry VIII of England and his third wife, Jane Seymour. Henry VIII had two other female heirs, Mary (aka "Bloody Mary") and Elizabeth (later Queen Elizabeth I). Edward VI was only 9 years old when he became king and he died when he was 15, so during his life, England was ruled by a Council since the king never reached maturity.
I believe Mark Twain purposefully chose to write about a child king because as a child, the fictional king always maintained his purity of heart. He never grew up and became a corrupted adult. In a sense, Edward VI is like Huck Finn. He is a child, like Huck, who really has more wisdom that the adults that surround him. At the end of the novel, Twain writes:
Yes, King Edward VI. lived only a few years, poor boy, but he lived them worthily.
The fictional Edward VI was able to appreciate the plight of his people, unlike many of his "adult" advisors. Even though he was a child king, he had suffered because he had lived among the people. At the end, the fictional Edward tells his critical advisors:
"What dost thou know of suffering and oppression? I and my people know, but not thou."
Read about the novel here on enotes.