Short answers, pulled from the story.
William Rankine, a Scottish engineer and physicist, coined the term "potential energy" in 1853. He chose it as part of the pairing "actual" versus "potential," tracing back to Aristotle's concept of potentiality. In 1867 he described potential energy as the "energy of configuration."
The main types are gravitational potential energy, elastic potential energy, electric potential energy (including electrostatic and magnetic), chemical potential energy, and nuclear potential energy. Each is associated with a different type of conservative force.
A conservative force is one where the total work done on a body moving between two points does not depend on the path taken - only the start and end positions matter. This path-independence is what allows a potential energy value to be assigned to every point in space, making potential energy a well-defined concept.
Gravitational potential energy is negative when physicists set the zero reference point at infinite separation between two masses. This convention is preferred because the alternative - setting zero at zero distance - produces infinite potential energy values at every real distance, making calculations impossible.
Dinorwig in Wales operates two lakes at different elevations. During periods of surplus electricity, water is pumped to the upper lake, converting electrical energy into gravitational potential energy. At peak demand, the water flows back through generator turbines, releasing that stored energy as electricity.
The Sun fuses 600 million tonnes of hydrogen nuclei into helium nuclei every second. The process results in a mass loss of roughly 4 million tonnes per second, which is released as kinetic energy and gamma rays that keep the solar core hot.