Short answers, pulled from the story.
The first centaur was born from the union of Ixion, a king of the Lapiths, and Nephele, a cloud goddess who had taken the form of Hera to trick Ixion. This unnatural union created the first generation of centaurs with the upper body of a human and the lower body of a horse. Another version of the myth suggests that the first centaur was Centaurus himself, a man who mated with the Magnesian mares.
The centaurs lived in the mountains of Thessaly, specifically in the region of Magnesia and on Mount Pelion. They also inhabited the Foloi oak forest in Elis and the Malean peninsula in southern Laconia. These locations were chosen to reflect their wild and untamed nature as they embodied the raw forces of nature.
The Centauromachy was a great battle that took place on the wedding day of Pirithous, the king of the Lapiths, and Hippodamia. The centaurs became drunk on wine and attempted to carry off the Lapith women, including Hippodamia, leading to a brutal struggle. Theseus assisted Pirithous in the battle, and the centaurs were driven off or destroyed, becoming a symbol of the struggle between civilization and barbarism.
Chiron was the son of Cronus and the nymph Philyra, and he was the only immortal centaur who possessed great wisdom and knowledge. He taught heroes such as Achilles, Jason, and Asclepius in a cave on Mount Pelion before being killed by an arrow dipped in the blood of the Hydra. Chiron gave up his immortality to Prometheus to end his suffering, and Prometheus was being punished by Zeus for stealing fire from the gods.
Female centaurs, called centaurides or centauresses, are not mentioned in early Greek literature and art but appear occasionally in later antiquity. A Macedonian mosaic of the 4th century BC is one of the earliest examples of the centauress in art. Ovid also mentions a centauress named Hylonome who committed suicide when her husband Cyllarus was killed in the war with the Lapiths.
In Greek art of the Archaic period, centaurs are depicted in three different forms designated by Professor Paul Baur. Class A centaurs have a human torso attached to the body of a horse at the withers, Class B centaurs have a human body and legs joined at the waist to the hindquarters of a horse, and Class C depicts centaurs with human forelegs terminating in hooves. These forms appeared in pottery, mosaics, and sculptures from the Bronze Age through the medieval period.