Short answers, pulled from the story.
A machine is a thermodynamic system that uses power to apply forces and control movement to perform an action. The term applies to artificial devices such as engines and motors, and also to natural biological macromolecules called molecular machines. Machines can be driven by animals, human power, wind, water, or chemical, thermal, and electrical power.
The six simple machines are the wedge, the inclined plane, the wheel and axle, the lever, the pulley, and the screw. Renaissance natural philosophers identified these six elementary devices that put a load into motion. The wedge is the oldest, and the screw was the last to be invented.
The wheel and axle was invented in Mesopotamia during the 5th millennium BC, and the lever appeared in the Near East around 5,000 years ago. The earliest pulleys date to Mesopotamia in the early 2nd millennium BC and to Egypt during the Twelfth Dynasty, 1991 to 1802 BC. The screw first appeared in Mesopotamia during the Neo-Assyrian period, 911 to 609 BC.
The Greek philosopher Archimedes discovered the principle of mechanical advantage in the lever around the 3rd century BC. He studied three of the simple machines: the lever, pulley, and screw. Later Greek philosophers defined the classic five simple machines and roughly calculated their mechanical advantage.
The Italian scientist Galileo Galilei worked out the complete dynamic theory of simple machines in 1600 in Le Meccaniche, or On Mechanics. He was the first to understand that simple machines do not create energy but merely transform it. Earlier Greek understanding had been limited to statics, the balance of forces.
Molecular machines are biological macromolecules that behave like machines inside living cells. Myosin reacts to ATP and ADP to drive muscle contraction, kinesin transports vesicles along microtubules, and ATP synthase spins like a turbine to synthesise ATP. A motile cilium is described as a nanomachine composed of perhaps over 600 proteins.
The earliest programmable machines came from the Muslim world. The Banu Musa brothers described an automated flute player, a music sequencer, in their Book of Ingenious Devices in the 9th century. In 1206, Al-Jazari invented programmable automata and robots, including four automaton musicians driven by a programmable drum machine.