Short answers, pulled from the story.
Poseidon fathered Pegasus as the horse-god while Medusa lay dead on the ground. The white stallion rose from the blood of Medusa's neck alongside his brother Chrysaor at the springs of Oceanus.
Bellerophon fell from the back of the flying steed while trying to reach Olympus. Both figures were said to have died by the hands of Zeus for their hubris after riding together to defeat the Chimera monster near Mount Helicon.
A single feather fell to Earth and landed near the city of Tarsus in modern Turkey on the day of his transformation into a constellation. Aratus recorded this event in his Phaenomena text over two thousand years ago.
During the Normandy invasion on the night of the 5th of June 1944, soldiers captured a bridge over the Caen Canal. They held it at all costs ahead of the seaborne assault and that structure became known forever as Pegasus Bridge.
Ecuador launched a weather satellite named Pegaso on the 26th of April 2013. Russian space debris damaged the craft shortly after deployment.