Great work.
I would like as many variables as possible exposed in the material/shader dialog in the inspector.

By frame per pixel, I mean that the number of sprites in the animations would be decreased, to there's a more pronounced step between animation keyframes, not as smooth as it is now (where there is one sprite per frame). I'm using sprite animation lingo here of course to get the point across.

If the animation speed is decreased, it would only make exactly that: The animation goes slower. What would be needed is a decrease in the number of different particle stages that are generated, coupled with an increase of time each stage is drawn.

For example, if the explosion is goes through ten stages, getting bigger each state:

1-2-3-4-5-6-7-8-9-10

Now, it skips a few steps but each step is drawn longer:

1-1-3-3-5-5-7-7-9-9

That's a great shader, I love it. I can see it be a moderate success on the Unity marketplace (moderate because it does caters to a niche, after all). On the other hand, I wouldn't mind getting my hands on this shader for free *whistles*

My girlfriend does 3D art like this:
https://jengy.carbonmade.com/projects/5522151

I think it's what she would loosely refer to as painting "baked" lighting.
Meaning its light/shadow that's a static part of the texture, and not rendered in real time.
Baking lighting can also refer to converting real time lighting into a texture.
And usually its a bit of both.
Before painting, baking on some lights can help you to identify the unwrapped parts of your model on the texture map easily.

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If a texture on a model is not affected by lighting, this is commonly called "unlit", at least in Unity (Unlit shader). "Fullbright" might also be used.

I wouldn't call it unlit, because you can apply any sort of shader over the top of this.
The texture acts as a base contrast that makes the object clear under any non perfect lighting conditions.
But you're right, many games with heavy painting style textures use a shader that diplays the texture and nothing more.

I would differ in that "baked lighting" refers specifically to textures where the lighting has indeed been baked into the bitmap with the 3d modeling/rendering application, not just by painting shadows and highlights in Photoshop.

You could make the bats a less-realistic but better readable color, like purple or deep blue, or brown.