Short answers, pulled from the story.
Philo of Byzantium wrote about water-driven wheels in his technical treatises Pneumatica and Parasceuastica around 280 BC. These documents contain the earliest known evidence of a water-powered wheel, predating later Arabic interpolations by centuries.
The Domesday Book compiled in 1086 recorded 5,624 watermills in England alone. Later research estimates this number should be considered a minimum of 6,082 since northern reaches were never properly recorded.
The Barbegal complex in southern France featured sixteen overshot waterwheels powering an equal number of flour mills. This facility produced 4.5 tons of flour per day for the town of Arelate.
Mathematician and engineer Zu Chongzhi erected a watermill in 488 AD which Emperor Wu of Southern Qi inspected. Engineer Yang Su of the Sui dynasty operated hundreds of them by the beginning of the 6th century.
Overshot wheels were later innovations around two and a half times more efficient than undershot types. Undershot wheels suffered inherent inefficiency because the wheel entered water behind main thrust then lifted out ahead of it.