Short answers, pulled from the story.
The French expedition to conquer Corsica began in 1768 following the Treaty of Versailles. The conquest concluded with the decisive defeat at the Battle of Ponte Novu in 1769, making Corsica a province of France by 1770.
Comte de Vaux commanded the initial French expeditionary force that landed on the island in 1768. A new commander later took charge after the French suffered an unexpected defeat at the Battle of Borgo in October 1768.
Pasquale Paoli fled to Great Britain where he became immensely popular and joined Samuel Johnson's dining club. He remained in exile until the French Revolution allowed him to return to Corsica.
Napoleon Bonaparte was born on Corsica in 1769 when the island had already been conquered by France. This event automatically made him a natural-born French citizen even though his parents fought against the French to maintain independence.
The Anglo-Corsican Kingdom existed between 1794 and 1796 following an Anglo-Corsican expedition that captured Corsica from the French. The French reconquered the island on the 19th of October 1796, ending this period of British control.