Short answers, pulled from the story.
Buddhism was officially introduced to the Japanese archipelago around 552 CE when a diplomatic mission from King Seong of Baekje arrived carrying an image of the Buddha Shakyamuni and ritual banners. This event marked the beginning of the religion's presence in the country during the middle of the sixth century.
The Soga clan became the first patrons of Buddhism in Japan after Emperor Kinmei allowed them to test the practice while other officials opposed it. The powerful Soga no Iname supported the new faith alongside immigrant groups like the Hata clan who brought expertise in Chinese technology and intellectual culture.
Six great schools emerged during the Nara period including Ritsu Vinaya Jōjitsu Kusha-shū Sanronshū Hossō and Kegon all continuations of Chinese Buddhist traditions. These schools were centered around the capital where great temples such as Asuka-dera and Tōdai-ji were erected under the kokubunji system established by Empress Genme in 710.
The Meiji government adopted a strong anti-Buddhist attitude starting in 1868 with the Kami and Buddhas Separation Order which dismantled combined temple-shrine complexes existing for centuries. This persecution known as haibutsu kishaku resulted in the destruction or closure of an estimated 40,000 temples reaching 80% of certain places between 1869 and 1871.
Two major Zen schools emerged during the Kamakura period: Rinzai founded by Eisai emphasizing Kōan practice and Sōtō founded by Dōgen emphasizing Shikantaza meditation. All major founders of new lineages during this era were ex-Tendai monks who had trained at Mt. Hiei studying both exoteric and esoteric systems of Tendai Buddhism.