Short answers, pulled from the story.
Taoism, also spelled Daoism, is a philosophical and religious tradition indigenous to China that emphasizes harmony with the Tao. The word Tao, written 道, has been translated as way, road, path, or technique, and Taoists understand it as an enigmatic process underlying reality that ultimately cannot be named.
Tradition holds that Laozi founded Taoism and wrote the Tao Te Ching, composed between the 4th and 6th centuries BCE, though his historicity is disputed and many scholars see him as a legendary figure. Many Chinese Taoists instead credit the Yellow Emperor, and the first organized form, the Way of the Celestial Masters, traces to Zhang Daoling and a vision of Laozi in 142 CE.
Tao and Dao are rival romanizations of the same Chinese word, 道. Tao comes from the Wade-Giles system, dominant in English until the late 20th century, while Dao comes from Hanyu Pinyin, adopted in China in the 1950s and by the Library of Congress in 2000, which now prevails in academic sources.
The Three Treasures, or Three Jewels, are ci, usually translated as compassion, jian, usually translated as moderation, and bugan wei tianxia xian, usually rendered as humility. Arthur Waley applied them to the social sphere as abstention from aggressive war and capital punishment, absolute simplicity of living, and refusal to assert active authority.
Wu wei is a primary ethical concept in Taoism, translated as non-action, effortless action, or non-interference. It is associated in ancient texts with water and the effortless way it flows around obstacles, and it means placing one's will in harmony with the natural way of the universe so goals can be achieved without forceful interference.
Taoism is one of five religious doctrines officially recognized by the Chinese government, with the Chinese Taoist Association regulating its activities in mainland China. It also has official status in Hong Kong and Macau and is a major religion in Taiwan, with significant populations of adherents throughout the Sinosphere and Southeast Asia.
In Komjathy's simplified Taoist pantheon, the Dao stands at the top as the uncreated source, followed by the Three Pure Ones and then the Jade Emperor, who administers the cosmos through a celestial bureaucracy. Taoism also venerates xian, or immortals, and zhenren, perfected persons, who are seen as the pinnacle of disciplined self-cultivation.