Short answers, pulled from the story.
The Return of the King won all eleven Academy Awards for which it was nominated at the 76th Academy Awards in 2004. This ties it with Ben-Hur and Titanic for the most Oscar wins ever, and it holds the record for the highest clean sweep in Oscar history, surpassing the nine-award records of Gigi and The Last Emperor.
Yes, The Return of the King was the first fantasy film to win the Academy Award for Best Picture. It won that award at the 76th Academy Awards ceremony in 2004.
The film grossed $1.118 billion in its initial theatrical run, becoming the highest-grossing film of 2003 and only the second film in history to cross the $1 billion mark, after Titanic in 1998. Following subsequent reissues, the total reached $1.148 billion.
The film was shot entirely in New Zealand. Principal photography ran from the 11th of October 1999 to the 22nd of December 2000, concurrent with the other two films in the trilogy, followed by six weeks of pick-up shoots in 2003.
Howard Shore composed the score. It was the most expansive of the three films in the trilogy, using the London Philharmonic Orchestra, the London Oratory School Schola, a mixed choir of 85 singers, a boy choir of over fifty members, and an instrument invented specifically for the film: a fiddle with four pairs of strings instead of single strings. The end title song "Into the West" was performed by Annie Lennox and won the Academy Award for Best Original Song.
The world premiere was held at Wellington's Embassy Theatre on the 1st of December 2003. It was estimated that over 100,000 people lined the streets, which was more than a quarter of Wellington's population at the time.