Here's a root of Ch'an: http://en.wikipedia.org/wiki/Lankavatara_Sutra

Buddhism is a child of Hinduism.

Taoism is particularly Chinese and is closer to more shamanistic practices in it's earlier iterations.

The was various intercourse obviously, But Buddhism didn't gain a seat in China until about 1000 years after it was already in full swing in India and throughout south and south east asia.