Short answers, pulled from the story.
The sound of a brass instrument comes from the player's lips vibrating against a metal cup. This mechanism is known as a lip reed and turns the human mouth into the primary oscillator of the instrument.
The first piston valve instruments appeared shortly after 1800, with Heinrich Stölzel introducing his design in 1814. By 1864, a core standard three-valve layout had become almost universal.
Cylindrical bore instruments like the trumpet produce a brighter and more penetrating tone, while conical bore instruments like the French horn produce a mellow and rounded tone. The geometry of the bore dictates the character of the instrument.
The combination of valves lowers the pitch by adding specific lengths of tubing, which creates intervals that are not perfectly aligned with the standard twelve-tone scale. This results in pitches that are significantly sharp, requiring players to use triggers or hand position to correct the pitch.
Traditionally, instruments are made of brass which is polished and lacquered to prevent corrosion. Higher quality models often feature gold or silver plating, while the 2010s saw the emergence of plastic instruments as a cheaper and more robust alternative.