Short answers, pulled from the story.
Bellerophon was a divine Corinthian hero of Greek mythology, the son of Poseidon and Eurynome, and the foster son of Glaukos. He was described as "the greatest hero and slayer of monsters, alongside Cadmus and Perseus, before the days of Heracles." His most famous feats were killing the Chimera and taming the winged horse Pegasus.
Bellerophon mounted a large block of lead onto his spear and flew toward the Chimera on Pegasus. He drove the lead into the creature's throat; the Chimera's own fire-breath melted the lead, which blocked its airway and suffocated it. Some ancient Greek red-figure pottery painters depicted him using Poseidon's trident rather than a lead-tipped spear.
The seer Polyeidos advised Bellerophon to sleep in the temple of Athena. In a dream, the goddess left a golden bridle beside him and told him to find Pegasus at the spring of Pirene on the citadel of Corinth. Waking to find the bridle real, Bellerophon went to Pirene and used the charmed bridle to tame the winged horse.
The name Bellerophon is disputed. Geoffrey Kirk interpreted it as "slayer of Belleros," referring to a Corinthian man Bellerophon accidentally killed while practicing knife-throwing. Other scholars read it as "bearing darts" or "slayer of monsters." The name appears to derive from roots meaning "projectile" or "dart" combined with a word for "slayer."
Bellerophon attempted to ride Pegasus all the way to Mount Olympus, seeking to join the gods. Zeus, angered by this presumption, sent a gadfly to sting Pegasus. The horse threw Bellerophon, and he fell back to earth. According to one version he died from the fall; in another he survived but was blinded after landing in a thorn bush, spending the rest of his life wandering in Cilicia.
Euripides wrote a tragedy called Bellerophon, now lost, but around thirty quotations survived in other ancient texts. The tragedy centered on Bellerophon's attempt to storm Olympus on Pegasus. A surviving passage shows Bellerophon apparently doubting the existence of the gods, which led Aristophanes to accuse Euripides of "atheism."