Short answers, pulled from the story.
The blind god Höðr killed Baldr by throwing a weapon made from mistletoe, guided by Loki. Loki had learned that mistletoe was the one object Frigg had not made swear an oath of protection over her son, and he fashioned the weapon himself. Odin and the goddess Rindr then fathered Váli specifically to avenge Baldr's death; Váli slew Höðr within a day of being born.
Baldr's mother Frigg traveled the world and extracted a vow from every object, alive and dead, never to harm her son. The only exception was mistletoe, which she had not asked because it seemed too small and unthreatening. Scholar Merrill Kaplan has proposed an alternative reading: that the omission echoes the legal practice of excluding young people from sworn oaths, making them a latent threat.
No one other than Odin knows what he whispered into Baldr's ear as the body was carried to the ship Hringhorni. The content was considered unknowable and became an unanswerable riddle Odin used against the giant Vafthrudnir in the Eddic poem Vafthrudnismal and in the riddles of Gestumblindi in Hervarar saga.
Hringhorni was described as the greatest ship ever built and belonged to Baldr. It served as his funeral pyre after his death. The gods could not push it into the sea, so they summoned the giantess Hyrrokin, who arrived on a wolf and launched the ship with a single push powerful enough to strike fire from the rollers and shake the earth.
Hel agreed to release Baldr on one condition: every object, alive and dead, must weep for him. All did except a giantess named Þökk, who refused to mourn. The sources generally identify Þökk as Loki in disguise. Because of that single refusal, Baldr remained in the underworld until after Ragnarök.
Saxo Grammaticus, writing at the end of the 12th century, presented Baldr, called Balderus, as a historical demigod rather than a god. In Saxo's account, Balderus and a rival named Høtherus competed for Nanna, the daughter of Gewar, King of Norway. Høtherus eventually wounded Balderus with a magic sword received from Mimir, and Balderus died three days later, being buried with royal honors in a barrow.