Short answers, pulled from the story.
Hatfield House was built by Robert Cecil, 1st Earl of Salisbury, who served as chief minister to King James I, and was completed in 1611. Cecil employed Robert Lemynge to supervise construction, with contributions from royal surveyor Simon Basil and Inigo Jones, who visited the site in October 1609.
Queen Elizabeth's Oak is a tree in the grounds of Hatfield House said to be the spot where Elizabeth I was told she had become queen of England. The tradition is considered unlikely by historians, since Mary I died in November and it is improbable that Elizabeth was sitting outside at that time of year.
The Royal Palace of Hatfield, built in 1497 by Cardinal John Morton, Archbishop of Canterbury and chief minister to Henry VII, stood on the site before the current Jacobean house. It comprised four wings surrounding a central courtyard; Henry VIII seized it from the church, and Robert Cecil demolished three of its wings in 1608 to make way for the present structure.
In 1548, when Elizabeth was fifteen years old, she was interrogated at Hatfield by Robert Tyrwhit, an agent of Edward VI, over suspicions that she had secretly agreed to marry Thomas Seymour. Elizabeth defended herself with wit and defiance, and Seymour was put to death in 1549 for numerous other crimes against the crown.
During World War II, Hatfield House served as the headquarters of Britain's first Civil Resettlement Unit, a program created to help repatriated prisoners of war return to civilian life. On the 12th of July 1945, the king and queen visited the unit at Hatfield, generating significant press coverage.
Hatfield House has been used as a filming location for numerous productions, including Greystoke: The Legend of Tarzan, Lord of the Apes (1984), Batman (1989), Shakespeare in Love (1998), Elizabeth: The Golden Age (2007), Sherlock Holmes (2009), The Favourite (2018), and Bridgerton (2020). The house has also appeared in The Crown, Enola Holmes, Pride and Prejudice and Zombies, V for Vendetta, and many others.