Short answers, pulled from the story.
A watermill is a structure that uses hydropower, driving a water wheel or water turbine to power a mechanical process such as milling, rolling, or hammering. Water is diverted from a river or mill pond along a channel to the wheel or turbine, whose movement rotates an axle that drives the mill's machinery, with spent water leaving through a tail race.
The Greeks invented the two main components of the watermill, the waterwheel and toothed gearing. The historian M.J.T. Lewis assigns the horizontal-wheeled mill to the Greek colony of Byzantium in the first half of the 3rd century BC and the vertical-wheeled mill to Ptolemaic Alexandria around 240 BC. The earliest evidence of a water-driven wheel appears in the treatises of Philo of Byzantium, who lived around 280 to 220 BC.
An undershot wheel sits in the flow of the mill race and is less efficient because it enters the water behind the main thrust and lifts out ahead of it, impeding itself. An overshot wheel brings water to the top of the wheel to fill buckets whose weight turns it, making it around two and a half times more efficient than the undershot.
The Domesday Book, compiled in 1086, records 5,624 watermills in England, though later research estimates a minimum of 6,082 because the northern reaches of England were never properly recorded. By 1300 the number had risen to between 10,000 and 15,000.
Barbegal, in southern France, was a 2nd century AD mill complex described as the greatest known concentration of mechanical power in the ancient world. It featured 16 overshot waterwheels driving an equal number of flour mills, with capacity estimated at 4.5 tons of flour per day, enough bread for the 12,500 inhabitants of the town of Arelate.
Cheap electrical energy made watermills obsolete in developed countries by the early 20th century, but some still operate. Historic mills run for demonstration and small-scale commercial milling, while an estimated 25,000 operate in Nepal and 200,000 in India for processing grain.
A tide mill traps water behind a mole or causeway built across the mouth of a small bay. Gates open at low tide to let the bay fill, then close at high tide to trap the water, and a sluice gate is later opened so the draining water drives the mill wheel. Tide mills work best where the tidal range is great, such as the Bay of Fundy in Canada, where tides can rise fifty feet.