Short answers, pulled from the story.
Buddhism arrived in Korea in 372 CE, when the monk Sundo was sent by Fu Jian of Former Qin to the court of King Sosurim of Goguryeo. The faith reached the kingdom of Baekje in 384 CE and the kingdom of Silla by the 5th century.
Tongbulgyo, meaning interpenetrated Buddhism, is a distinctly Korean synthesis that sought to harmonize disputes among different Buddhist schools through a principle called hwajaeng. Early Korean practitioners developed it to resolve what they saw as inconsistencies within the Mahayana traditions they received from China and India.
Jinul, who lived from 1158 to 1210, was the most influential figure in Goryeo-period Seon Buddhism. He founded a reform community at Songgwangsa on Mt. Jogye and formulated the dictum of sudden enlightenment followed by gradual practice. The hwadu meditation method he introduced from Dahui Zonggao remains the main practice in Korean Seon today.
The Tripitaka Koreana is a woodblock edition of the Buddhist scriptures produced in two editions during the Goryeo period. The second edition, completed between 1214 and 1259, survived after the first was destroyed in a Mongol attack in 1232. It is kept at Haeinsa in Gyeongsang and served as the standard version of the Tripitaka in East Asia for nearly seven hundred years.
When Japanese forces invaded between 1592 and 1598, Seon monks organized guerrilla units under a movement called the uisa, or righteous monks. Several thousand monks eventually joined, led by the Seon master Seosan Hyujeong. Their participation was considered a critical factor in the eventual expulsion of the Japanese invaders.
The Jogye Order is fully celibate and is the largest sect of Korean Buddhism by clergy and adherents; it changed its ceremonial robe to brown in 1970 to distinguish itself. The Taego Order includes both celibate and married clergy, retains the traditional red kasa, and is the only order that maintains the full traditional Korean Buddhist ritual tradition including forms such as Yeongsanjae.