1. Empress Xiaomei is the granddaughter of the Shangguan family on her paternal side that was massacred by Huo Guang, their in-laws. Yes her mother is Huo Guang's eldest daughter, the one who killed herself after her husband who is a Shangguan was killed by her father's own sword. This is why we get the heartbreaking scene at the end of that episode where she is crying over her family's bloodbath quietly in her own royal chamber a presumably safe place, but the Emperor advises her to hide her feelings because they are all being constantly watched and nobody is safe from imperial politics, not even family.
2. From what I've seen so far, the series did not reveal her family name once, but Yun Ge is actually a Huo herself. If you have never read the book or know that this is a sequel to Sound of the Desert, she is actually the daughter of the prequel's OTP - Jin Yu (mother) and general Huo Qu Bing (father, who is Huo Guang's older brother). Which makes Huo Guang her uncle and nemesis Huo Cheng Jun her cousin all along. If the drama stays faithful to the events of the novel, eventually even the characters themselves will be taken in for a real surprise.
3. Previous Emperor killed Ling Gege's mother Concubine Zhao because he was due to pass his throne to his youngest son Liu Fuling who was 8 years old at that time, and from what he observed a young child very dependent and attached to his mother (ffs, just a normal loving mother-son relationship). In his mind, this cannot be allowed for a soon-to-be ruler of the country and he just wants to make the young Fuling independent and ready for the throne.
4. Meng Jue's younger brother was substituted in place for a young Liu Bingyi whom who would'v been killed along with the rest of his family as part of the infamous Crown Prince Ju massacre.
https://en.wikipedia.org/wiki/Liu_Ju For more historical background information on the events leading up to it. But the series gave a shorter (and less accurate) version of it in that Crown Prince was falsely framed for witchcraft against his own father the Emperor and seeing that witchcraft was all the malicious deal back in the day it was enough reason to kill his son and everyone related on a whim!
Hope that answered your questions !