Short answers, pulled from the story.
Murasaki Shikibu was born around 973 into the northern Fujiwara clan, a family that had slipped from the highest echelons of power to the middle ranks of the aristocracy. Her father, Fujiwara no Tametoki, was a scholar and minor official who allowed her to study Chinese classics despite societal norms that restricted female education.
Murasaki Shikibu married Fujiwara no Nobutaka in her mid-to-late twenties, and he died during a cholera epidemic in 999, two years after the birth of their daughter Kenshi. Her husband was significantly older, already had multiple households, and was known for his extravagant dress and talent as a dancer.
Murasaki Shikibu was invited to serve as a lady-in-waiting to Empress Shōshi in 1005, a position secured by the powerful Fujiwara no Michinaga. She worked in a hostile environment alongside other women like Izumi Shikibu and Sei Shōnagon while navigating intense political maneuvering at the Imperial court.
The Tale of Genji was written between 1000 and 1012 and spans 54 chapters across 1100 pages. The work was considered complete by 1021 and became a subject of scholarly criticism within a century of its completion.
Most scholars agree that Murasaki Shikibu died in 1014, though others suggest she was alive as late as 1025. Her father made a hasty return to Kyoto in 1014, possibly because of her death, and her daughter Kenshi entered court service in 1025.