The music heard at the end is the prelude from Verdi's 'La Traviata', the story of a woman who also immerses herself in high society and is eventually consumed by it.
Balmoral Castle, together with Sandringham House, is the private property of the Queen and is not part of the Crown Estate. The Balmoral estate and its original castle (demolished) were bought by Prince Albert, the husband of Queen Victoria, Elizabeth II's great-great-grandmother, in 1852.
The home passing as Balmoral is Ardverkie House in Newtonmore, Highland, Scotland and is also featured in Monarch of the Glen (2000) and Salmon Fishing in the Yemen (2011).
Diana is chaperoned on her date to the opera by her granny. Traditionally, highborn young ladies in England would be chaperoned by their mothers or other female relatives as they searched for husbands during the London Season. Queen Elizabeth abolished the presentation of debutantes at court in 1958, and Queen Charlotte's Ball subsequently ended in 1976, around the time Diana would have been of an age to attend London balls.