Short answers, pulled from the story.
Masamune was a medieval Japanese blacksmith active mainly between 1288 and 1328, working in Sagami Province during the Kamakura period. He is widely regarded as Japan's greatest swordsmith, known for creating tachi and tantō in the Sōshū school. Nine of his works are designated National Treasures of Japan.
The Honjo Masamune was surrendered to a police station in Mejiro in December 1945 by its last known owner, Tokugawa Iemasa, under the American occupation's sword surrender order. In January 1946 it was handed to a man identified as Sgt. Coldy Bimore of the Foreign Liquidations Commission of AFWESPAC. Its location has been unknown ever since.
The Juttetsu, or Ten Great Disciples of Masamune, are a group of ten swordsmiths out of the roughly fifteen he is believed to have trained. They include Shizu Saburo Kaneuji, Kinju, Go Yoshihiro, Saeki Norishige, Saemonzaburo, Kunishige, Kunitsugu, Naotsuna, Chogi, and Kanemitsu. Their work spread the Sōshū tradition into regional schools across Japan including the Mino, Echizen, and Chikuzen traditions.
The Kyōhō Meibutsuchō lists 59 swords attributed to Masamune out of a total of 248 entries, representing roughly one quarter of the entire catalogue. Of those 59, 18 had already been lost at the time of compilation. Supplemental volumes added two more, bringing the attributed total to 61.
The legend describes a test where both smiths suspended their swords in a creek with the cutting edge against the current. Muramasa's blade cut everything that passed, while Masamune's left fish unharmed and cut only leaves. A watching monk declared Masamune's sword the finer of the two because it did not cut the innocent. Historians note the two smiths could not have actually met given the dates of their active careers.
The Masamune Prize is an award presented at the Japanese Sword Making Competition to a swordsmith who has created an exceptional work. It is not awarded every year, only when a blade of sufficient quality is produced.