Short answers, pulled from the story.
Astronomical filters have been used in astronomy at least since the solar eclipse of the 12th of May 1706, making that event one of the earliest documented instances of filtered astronomical observation.
Eyepiece solar filters thread into position behind the lens, close to the observer's eye, and do not prevent heat from building up inside the telescope body. According to NASA, these glass filters can crack unexpectedly from overheating when the telescope is pointed at the Sun, and retinal damage can occur faster than the observer can move the eye from the eyepiece.
The Wratten system is the standard numbering system used to identify color filter types for astronomical use. It was first manufactured by Kodak in 1909 and assigns a number to each filter to indicate its color and application, such as the number 8 yellow filter used to show Mars's maria and Jupiter's belts.
Narrowband astronomical filters typically transmit a bandwidth of 22 nanometers or less. Common targets include the H-alpha line at 656 nm, O-III lines at 496 nm and 501 nm, the Hydrogen-beta line at 486 nm, and the S-II line at 672 nm.
The HST-palette is a color-mapping scheme commonly used with the Hubble Space Telescope. It assigns red to the S-II filter, green to H-alpha, and blue to O-III, allowing astronomers to combine images from different emission-line filters into false-color images that reveal the chemical distribution inside nebulae.
Broadband, or light pollution reduction, filters block sodium and mercury vapor streetlight emissions and natural skyglow such as auroral light, making it possible to observe nebulae and galaxies from city and light-polluted skies. They are particularly suited to galaxy observation because their wider transmission range preserves enough brightness to reveal detail across the broad spectrum galaxies emit.