Short answers, pulled from the story.
Napoleon stayed at The Briars, a small pavilion in the garden of English merchant William Balcombe, for the first few weeks of his exile in late 1815. He was later moved to Longwood House.
Betsy Balcombe, whose full name was Elizabeth Lucia Balcombe, was the 14-year-old daughter of William Balcombe. She was the only member of the Balcombe family who spoke French and served as the family's translator during Napoleon's stay at The Briars.
Yes. The Duke of Wellington stayed at The Briars in 1805 on his return from a tour of duty in India, a decade before Napoleon's exile there. Wellington later wrote to the garrison admiral on the 3rd of April 1816, joking that he hoped Napoleon liked "his" rooms at the Balcombes.
The East India Company purchased The Briars in 1827 for six thousand pounds. They used the property for growing mulberry trees and making silk.
Dame Mabel Brookes, a great-granddaughter of William Balcombe, purchased the pavilion in 1959 and donated it to the French government. The French government appointed her Chevalier de la Légion d'honneur in 1960 in recognition of the gift.
William Balcombe is reported to have introduced the Sweet Briar (Rosa rubiginosa) and the Weeping Willow (Salix babylonica) to Australia on his estate in the Carwoola area of New South Wales. The willows are said to have been propagated from cuttings taken near Napoleon's grave on Saint Helena.