Short answers, pulled from the story.
Centaurs were born from the union of Ixion and a cloud shaped like Hera, or alternatively from Centaurus mating with Magnesian mares. These creatures lived wild in regions such as Mount Pelion and the Foloi oak forest across mainland Greece and Cyprus.
The conflict known as the Centauromachy erupted when centaurs attempted to carry off Hippodamia and other women at Pirithous wedding feast. Theseus assisted Pirithous in driving the centaurs away while Caeneus fought back against rocks and tree branches wielded by the beasts.
Palaephatus suggested ken plus tauros means piercing bull in On Incredible Tales while Alexander Hislop argued in 1853 that the term derived from Semitic Kohen and tor meaning to go round. Modern philologists reject this phonetic shift theory entirely without reaching consensus on the root meaning.
Mycenaean terracotta figures found at Ugarit tentatively identify as centaurs dating back to the Bronze Age. Winged centaurs appeared on amphorae and Dipylon cups during the Geometric period before Roman art preserved these images through centuries including the Great Cameo of Constantine circa AD 314, 16.
Kinnaras appear throughout Indian texts as half-men half-horses with man-torsos atop equine bodies according to Devdutt Pattanaik documentation. A legend from Thiruvananthapuram describes a Yadava prince transformed by a Brahmin's curse into a creature with a horse body and human head.