I haven't finished the novel, but here's what I know so far.
The Imperial Family's surname is Liu (刘), not Liu Miantang's Liu (柳) though. They are the ruling imperial power of the Great Yan Empire. The current emperor's name in the novel was Liu Tang. I don't knows if he's a child like in the drama. Some comments said they don't remember a child emperor mentioned in the novel.
The Cui Family isn't related to the Royal Family, they earned their Wang title from contribution to the court. The Late Emperor bestowed the title of Huaiyang Wang / Lord Huaiyang to Cui Xingzhou 's father. He had many concubines and had 9 sons, CXZ being the youngest. Cui Xingzhou inherited his position as Lord Huaiyang from his father as he was the legitimate son born from the first wife. The novel said there was a bloody succession battle that left them with only 4 sons left. The Cui Family's fiefdom is Zhenzhou, which covers Lingquan Town, the novel said it's in Jiangnan. They ruled over the prefecture, but also serving the imperial court.
As of ep 12, another Wang has appeared, but this Wang is different as he was the Late Emperor's brother. Sui Wang / Prince Sui seems to plan sth big to overthrow the current ruling power. The drama having a child emperor would be even easier to install another emperor. (It's coming, yeah)
Liu Tang and his mother, Empress Dowager Wu (then Consort Xi) deposed the crown prince, and massacred a lot of people to sit on the throne. That's why we see Liu Yu / Ziyu, planning to do something "big". Yeah, he was that crown prince.