How does a screen work?

To me the magical part about CRTs is color. I don't quite understand how the shadow mask works. Like, yeah, there are three guns, one for each color channel, and the openings in the mask match their layout, and somehow the beam coming out of each gun can only ever hit its corresponding phosphor dots. Even after being deflected. But... how? Also, wouldn't the deflection coils affect each of the three beams slightly differently?

Each hole in the shadow mask acts as a pinhole camera, giving an inverted image (in electrons) of the three guns. All three beams get bent nearly the same amount, but yes there is some distortion which is traditionally corrected for by a set of convergence coils and corresponding circuit with knobs for static and dynamic convergence [0]. A pain to adjust, BTW.

[0] https://antiqueradio.org/art/RCACTC-11ConvergBoardNewRC.jpg

It's parallax, basically. The pigment dots and mask holes are positioned such that when you look from the perspective of the "red" electron gun (*), you only see red pigment dots. Move a couple cm to the "blue" gun and the parallax shift now makes you to see only blue pigment dots instead. Or from the other direction, no matter which "red" dot you stand at, you only see the "red" gun through "your" hole.

The exact sizes, shapes, and positions of the pigment dot triples (and/or the mask holes) are presumably chosen so that this holds even away from the main axis. Also, the shape of the deflecting field is probably tuned to keep the rays as well-focused as possible. Similarly to how photographic lenses are carefully designed to minimize aberrations and softness even far from the optical axis.

(*) Simplifying a bit by assuming that the beam gets deflected immediately as it leaves the gun, which is of course inaccurate.

For me it was the opposite. Learning how a monochrome CRT requires no mask sort of destroyed my world view of what a display had to have. pixels(even the quasi pixels as found in a color CRT mask) were not actually required or present.

As a result monochrome terminal text has this surprising sharpness to it.(surprising if you are used to color displays). But the real visual treat are the long persistence phosphor radar scopes.

That's the cool thing about analog video, it doesn't really have the concept of horizontal resolution. Especially when it's monochrome. It's made up of lines that continuously change brightness as they're drawn.

Color composite video, as far as I understand, does have a limit to the horizontal resolution because in all three standards the color information is encoded as a high-frequency signal added to the main (luminance) one, so that frequency is your upper limit on how quickly the luminance can change.

S-video, VGA, and component should, in theory, allow infinite horizontal resolution and color.