A few historical points if you're interested in this stuff, like me, or curious about the references! 

The drama is set during the reign of Zhao Ji, Emperor Huizong. This was arguably the cultural zenith of the Song, but also a period of increasing political corruption. Emperor Huizong was a highly cultured man who was also deeply interested in Taoism, and the discussions of the "auspicious sign" fit well within the ethos of his court.  The dominant politician for much of Huizong's reign was the senior grand councilor Cai Jing, whose sons also became highly influential. He's a notorious figure in Chinese history and classic novels, almost an archetypal corrupt official, though he was arguably something of a social reformer, as well.

Zhu Mian (called Zou Mian in the drama) was originally a crony of the Cai family who became immensely powerful in his own right. He was a merchant from Suzhou in the southeast and formed a partnership with the Cai family and the senior eunuch Tong Guan to transport exotic rocks and plants from the southeast to build a grand garden for Huizong, who was devoted to aesthetic pleasure. Despite the incredible corruption and oppressiveness of this system, Zhu used it to secure senior government offices and intermarriages with the imperial clan that made him the most powerful man in the south, and a key figure at court as well.

Bao Zheng (the man whose name is so visible on the honor roll of the Kaifeng Court) was a real figure who was a prominent court official and prefect of Kaifeng during the reign of Emperor Renzong, several decades before Emperor Huizong's reign. He was known for his strong ethics and is also a legendary figure in Chinese history and popular culture.  

Kaifeng was indeed a city teeming with vitality, commerce, high culture, and tumultuous politics during this period. It all ended very badly when the Jurchens invaded in 1126 and 1127, but until then, the dynasty was ostensibly strong and thriving. 

Thank you! While Justice Bao is probably well known among people who have interest in Chinese history, culture, arts and literature (stories on his "public cases" created a separate genre, called gong'an), Cai Jing and Zhu Mian could be less known... (I've never heard of them before)