Short answers, pulled from the story.
A wheel is a rotating component, usually circular, that turns on an axle bearing. Joined to an axle through a bearing, it forms the wheel and axle, one of the six simple machines, reducing friction by moving the frictional work from the travelled surface into the bearings.
The solid wooden wheel, a disk with a hole for the axle, dates to the late Neolithic. The Copper Age window of 4500 to 3300 BCE saw the potter's wheel, the earliest solid wooden wheels, and the earliest wheeled vehicles, while miniature clay wheels north of the Black Sea before 4000 BCE give the oldest indirect evidence.
The Ljubljana Marshes Wheel from Stare Gmajne near Ljubljana in Slovenia is dated within two standard deviations to 3340 to 3030 BCE, with its axle dated to 3360 to 3045 BCE. A wooden wheel about 1 metre across found at Must Farm in East Anglia in 2016, dated from 1100 to 800 BCE, is the earliest and most complete of its type in Britain.
The earliest known wooden spoked wheels come from the Sintashta culture at Krivoye Lake, dating to around 2000 BCE. The spoked wheel allowed lighter, swifter vehicles and enabled horse-drawn war chariots.
Mesoamericans built small wheeled toys, some near 1500 BCE, but never a wheelbarrow, potter's wheel, or other practical wheeled object. The likely obstacle was the absence of a large domesticated draft animal, since the bison resisted domestication and the llama was a pack animal unsuited to pulling wheeled vehicles.
Dragging a 100 kilogram object 10 metres over a surface with a coefficient of friction of 0.5 requires 4905 joules. Giving the object four wheels, with a 1000 millimetre wheel diameter and 50 millimetre axle, drops the work to 123 joules, about one fortieth of the dragging effort.
The wheel is a metaphor for cycles and repetition, appearing in the chakra, reincarnation, and Yin and Yang, and in the Kalachakra or wheel of time in some forms of Buddhism. It is the prominent figure on the flag of India, where it represents law or dharma, and it reappears on the flag of the Romani people.