Short answers, pulled from the story.
East Asian Buddhists constitute the numerically largest body of Buddhist traditions in the world, numbering over half of all Buddhists globally. The tradition encompasses Chinese, Japanese, Korean, and Vietnamese Buddhism.
The Chinese Buddhist Canon is the shared body of scripture used by East Asian Buddhist traditions. Translations began in the second century, and the collection evolved over roughly a thousand years. The first woodblock-printed edition was published in 983. A major modern edition, the Taisho Tripitaka, was produced in Japan between 1924 and 1932.
Buddhism reached Japan through Chinese and Korean influence in the 5th and 6th centuries. The Soga clan during the Asuka period helped legitimize the religion by constructing temples. Imperial patronage during the Nara period then drove further institutional growth.
Married clergy in some Japanese Buddhist sects is a result of the Meiji Restoration, when a nationwide government campaign against Buddhism forced certain Japanese sects to change their practices. Most East Asian Buddhist monastics follow the Dharmaguptaka Vinaya, a traditional monastic code that prohibits marriage.
Traditional scholars including Gyonen (1240-1321) enumerated thirteen schools. They include the Chan school (attributed to Bodhidharma), the Consciousness-Only school (founded by Xuanzang, 602-664), the Tiantai school, the Huayan school, the Pure Land tradition, and the Three Treatises school (founded by Kumarajiva, 344-413 CE), among others. Some schools are now defunct, while others such as Chan, Pure Land, and Tiantai remain active living traditions.
Buddhism was the state religion of Dai Viet under three successive dynasties: the Dinh dynasty (968-981), the Ly dynasty (1009-1225), and the Tran dynasty (1225-1400). The Truc Lam Thien school was founded in 1299 by Tran Nhan Tong, the third emperor of the Tran dynasty.