Short answers, pulled from the story.
The migration occurred in 1392 when professional people known as the Thirty-six families moved from Fujian Province. They brought advanced learning and skills including Chinese kenpō which became the origin of karate.
Ankō Itosu created Pin'an forms which are simplified kata for beginning students common across nearly all styles of karate. He helped get karate introduced into Okinawa's public schools where forms were taught to children at elementary school level in 1905.
The Okinawa Prefectural Assembly passed a resolution in 2005 designating the 25th of October as Karate Day. This decision commemorates the roundtable meeting held on the 25th of October 1936 where masters resolved to use the name karate meaning empty hand.
Shotokan karate became the most spread martial art in Italy apart from Judo by 1970. The Japan Karate Association sent four instructors to Europe in 1965 including Taiji Kase to France and Keinosuke Enoeda to England.
The International Olympic Committee approved karate as an Olympic sport in August 2016 beginning at the 2020 Summer Olympics. On the 3rd of August 2016 all five sports including baseball and softball were approved for inclusion in the 2020 Olympic program.