Short answers, pulled from the story.
Buddhist missionaries began bringing Buddhism to China during the Han dynasty, and the religion was present in China at the beginning of the common era. Mahayana Buddhism arrived in China through the Silk Route in the 1st century CE via Tibet.
The first surviving translations of Buddhist texts into Chinese were those of the 2nd-century Parthian An Shigao who worked in the capital of Luoyang. His work was followed by the extensive Mahayana translations of the Kushan monk Lokakshema active until 186 as well as the work of Dharmaraksha from the 3rd century.
The Great Anti-Buddhist Persecution occurred between 841 and 845 under Emperor Wuzong of Tang. It greatly impacted and weakened the Buddhist institutions in China due to the Chinese state's need for taxes and wealth.
The Tiantai school was mainly founded by the efforts of master Zhiyi who lived from 538 to 597 CE based on the Lotus Sutra. The Huayan school was based on the works of Chinese masters such as Dushun who lived from 557 to 640 Zhiyan who lived from 602 to 668 and Fazang who lived from 643 to 712.
Chinese Buddhism suffered extensive repression persecution and destruction during the Cultural Revolution from 1966 until Mao Zedong's death in 1976. Buddhist monks were attacked disrobed arrested and sent to camps while Buddhist writings were burned and temples systematically destroyed.