Short answers, pulled from the story.
Laozi was a legendary Chinese philosopher and sage traditionally credited with writing the Tao Te Ching, one of the foundational texts of Taoism. Traditional accounts identify him as Li Er, born in the 6th century BC in the state of Chu. Modern scholarship questions both his historicity and the attribution of the text to a single author.
Tradition says Laozi wrote the Tao Te Ching before departing to the west, but modern textual and historical scholarship dates the received text to the Warring States period, roughly 475 to 221 BC, and treats it as a composite work by many hands. The oldest manuscript fragments, the Guodian Chu Slips, date to the late 4th century BC and match only about one third of the received text.
Laozi, written 老子, is not a personal name but an honorific meaning 'old teacher' or 'venerable master'. The ending zǐ matches that of other ancient Chinese philosophers such as Kongzi, Mengzi, and Zhuangzi. Tradition gives him the personal name Li Er and the courtesy name Boyang.
Wu wei, literally 'non-action' or 'not acting', is a central concept of the Tao Te Ching. It carries multiple meanings, including not forcing, acting spontaneously, and flowing with the moment, and it explains ziran, or harmony with the Tao. On a political level it means avoiding war, harsh laws, and heavy taxes.
Because of his traditional name Li Er, Laozi was venerated as the ancestor of the Tang dynasty emperors, who traced their descent to him through the Longxi Li lineage. Emperor Gaozong named him the 'Supremely Mysterious and Primordial Emperor' in 666, and Emperor Xuanzong declared him the dynasty's 'Sage Ancestor' in 743.
In religious Taoism, Laozi is venerated as Taishang Laojun, one of the Three Pure Ones of the Taoist pantheon, and was worshipped as a god from the Han dynasty onward. Belief in the divine Laozi led to the Way of the Celestial Masters, the first organized religious Taoist sect. His birthday is popularly held on the 15th day of the second month of the Chinese calendar.
The economist Murray Rothbard suggested Laozi was the first libertarian, comparing his ideas on government to Friedrich Hayek's theory of spontaneous order. David Boaz included passages from the Tao Te Ching in his 1997 book The Libertarian Reader, citing Laozi's counsel that rulers should 'do nothing' so that men would dwell in harmony.