Short answers, pulled from the story.
The name Loki connects to the Germanic root luk- which denoted things to do with loops. This linguistic origin points to knots, hooks, closed-off rooms, and locks rather than an association with Old Norse logi meaning flame.
Chapter 34 of Gylfaginning introduces Loki as the son of Fárbauti and Laufey with brothers Helblindi and Býleistr. Sigyn is introduced as his wife with a son named Nari or Narfi while three children born to Angrboða include the wolf Fenrir, the serpent Jörmungandr, and the female being Hel.
A semi-circular flat stone discovered on a beach near Snaptun in Denmark dates to around 1000 CE. It features a mustachioed face with scarred lips that scholars identify as Loki due to his stitched lips referencing a tale where sons of Ivaldi sewed them shut.
Jan de Vries theorized in 1959 that Loki represents a typical trickster figure. This conclusion stands alongside other scholarly theories such as Jacob Grimm advancing the notion of Loki as a god of fire in 1835.
Chapter 42 details how Loki gives birth to Sleipnir after transforming into a mare when a stallion named Svaðilfari runs toward her. Later Loki produces a gray foal with eight legs from this union which allows the gods to kill the builder when he fails to complete the wall by summer.