Is it possible to self learn how to do pixel animation with this or is it more a case of, "so that's how they animate. That's quite cool"?
Hard question to answer as it might depend upon your base level and inclinations even then.
I do generally recommend
https://gdcvault.com/play/1023586/8-Bit-8-Bitish-Graphics
https://en.wikipedia.org/wiki/File:Lemming_animation.gif also says much despite being a small gif (right side is the released animation, left is what the devs had in there initially)
I am sure there is much to be gleaned from it, and tweaking it to see how something might fail, and creativity when faced with limitations (not so much a thing on PC or modern consoles really -- a sprite sheet a few thousand items long is likely less space than a few seconds of video or throwaway background NPC 3d texture).
More generally start with an item, you can go from a photo because why not, you will fail (though there are exceptions
https://doomwiki.org/wiki/Models ) and instead start to think of things to exaggerate and size and proportion (usually heads for expressive faces/eyes), animations are in some ways still like 3d in that they go from one to another (plus whatever exaggeration to make it look cool like that lemmings thing, stopping short of being too visually noisy which usually means about 3 points of movement*, it is space (generally or VRAM) and effort that stop it from being true stop motion in most games.
Rather than going from photo some will go for essence (usually those from a more conventional drawing background).
You will also have the translation, reflection, rotation, scale thing you would probably have learned on graphs in school. Bit more advanced comes acceleration (something drops and you don't start by moving 3 pixels a second and staying there until the end, reality starts moving slow and accelerating according to gravity), and in the words of a legendary internet reviewer you might not notice but your brain did.
*most people can only immediately visually count to three, very few any more than that. See also why 99% of all characters in all written languages are 3 strokes or less. It can also speak to colours but for that we probably get more general colour theory (
https://www.designmantic.com/blog/infographics/the-10-commandments-of-color-theory/ ) and design concepts, though again old school graphics from CGA on up might have had a more limited option for a lot of things and had to force things accordingly rather than doing gradients.
After this I also have favourites like
https://docs.google.com/document/d/1iNSQIyNpVGHeak6isbP6AHdHD50gs8MNXF1GCf08efg/pub
More time to do your animations/have the player react if the camera is placed correctly. Telegraphing attacks (say an enemy holding on the edge of the screen for a few seconds before darting in during brawlers) also being part of that.
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