Short answers, pulled from the story.
William Rankine introduced the term potential energy during a presentation to the Philosophical Society of Glasgow in 1853. He sought to create new terminology for the transformation of energy by contrasting actual versus potential states.
A conservative vector field expresses itself as the gradient of a scalar function known as a scalar potential. The potential energy relates to and derives from this potential function where work done against a force field increases potential energy.
An object at certain height above Moon surface has less gravitational potential energy than same height above Earth surface because Moon gravity is weaker. Local gravitational field strength measures 9.8 metres per second squared on Earth while factors include height relative to reference point, its mass, and strength of gravitational field.
Green plants transform solar energy to chemical energy through photosynthesis process. Fuel burned converts chemical energy to heat during reaction and electrical energy converts to chemical energy through electrochemical reactions.
Six hundred million tonnes hydrogen nuclei fused into helium nuclei per second in Sun core. Loss about four million tonnes mass per second liberated as heat and radiation in nuclear reactions.