Short answers, pulled from the story.
The electric guitar was invented in 1932. George Beauchamp, general manager of the National Stringed Instrument Corporation, designed the cast aluminium lap steel "Frying Pan" in 1931 with Paul Barth, and worked out the electromagnetic pickups together with Adolph Rickenbacker. Commercial production began in late summer 1932 by the Ro-Pat-In Corporation in Los Angeles.
The first electrically amplified stringed instrument marketed commercially was a cast aluminium lap steel guitar nicknamed the "Frying Pan". It was first used in a publicly promoted performance by Gage Brewer in Wichita, Kansas in October 1932.
An electric guitar uses one or more pickups, which are magnets wound with coils of very fine wire, to convert string vibration into a small electric current. That signal passes through the tone and volume controls to the output jack, then through a cable to an amplifier and loudspeakers, at a voltage usually around one to nine millivolts.
A solid-body electric guitar is made of solid wood with no functionally resonating air spaces, so the amplified sound reproduces string vibration alone. A semi-acoustic guitar has a hollow body whose vibrations combine with the string vibration in the pickups, often with a solid block through the soundbox to reduce feedback.
A humbucker is a double-coil pickup invented to reduce mains hum, the 50 or 60 cycles per second interference picked up by magnetic pickups. It is named because it "bucks", or opposes, the hum, and its high combined inductance also produces a richer, fatter tone.
The electric guitar became the most important instrument in popular music during the 1950s and 1960s. It was first adopted by jazz players who wanted single-note solos in big band ensembles, and it became a major component in electric blues, rock and roll, rock music, and heavy metal.