Citations are from "Wagon, Chariot, and Carriage" by Stuart Piggott ISBN 0500251142
China's vehicle technology can likely be traced to Transcaucasia (modern Azerbaijan) 1500 BC through Lchashen chariot (Ibid. 65) that resembles Chinese types
Chariotry is the first wheeled technology, plough tech is not attested til 384-221 BC (Warring States)
"Two-horse chariot quite suddenly appears in the archeology... for hunting, ritual parade and warfare" (Ibid. 63) of late Shang Dynasty 1200 BC.
For warfare, chariotry declines by late Western Zhou 1027-771 BC, while cavalry warfare comes into fashion 4th Century BC
10th Century Zhou texts describe a "royal conferral" of a "chariot of bronze fittings" with "gilt bridles and girth-straps" (Ibid. 68)
Later texts (what texts and when? idk) show a "chivalry culture" develops between Aristocrats with pre-arranged battlefields on either side
After being phased out for warfare, chariots are mainly used for aristocratic vanity "until well into Han times" (Ibid. 67)
It's unclear from the above two notes whether chariots were used for battlefields between aristocrats after being phased-out, but I'm assuming no. It would be nice to get a citation on Chinese chivalry culture after Zhou, but this book doesn't have one.