All graphics cards are dropping support/have dropped support for palettized (indexed) textures. It's no longer a technique that can be used. While you can do in inside the PNG file, as soon as you convert the image to a texture, the background will have to be filled in with full, non-indexed colors.
If your program doesn't have 16-24 bit image support, the problem is in the coding/settings. It has little, if anything, to do with your video card. Having a limited palette will save RAM simply because you require fewer bits to represent the same amount of data. That's why many doujin games either force your display into limited colour modes or ask you on startup if you want 16 or 32 bit colour.
Secondly, triangles for animation simply is not practical from a design standpoint. You're thinking like an engineer, not an artist. A 2D texture is not a 3D texture - the reason images are compacted is simply because you're dealing with 2D textures mapped onto 3D surfaces and it's an efficient use of space as the actual order of the 2D image is irrelevant. You can't do morphing, nor mapping with a 2D image, and it'd be absolute hell
to align properly.
It doesn't even save much space because of the nature of 2D images. Imagine animating a square. For you to represent a square in a triangle, you need to use a triangle with double the area of the square (don't argue with math). This loss is identical to that of trying to represent a triangle in a square. Unfortunately, animations are NOT STATIC
. Mathematically, we can approximate the area needed with a circle (i.e. all directions of expansion are equally likely!) and superimposing a circle within a triangle causes quite a lot more wasted space than a circle in a square. Anything more complicated than a square, and it ceases to tessellate properly, good luck coding a viewer for that (not to mention most if not ALL animation viewers do not support triangles).
With 3D models, this is not an issue because you are just mapping onto a model. Irregular shapes are fine. You can't really use 3D theory in 2 dimensions because simply specifying the limits of each separate irregular polygon would take FAR more memory than anything you'd ever save.Edit: Before you reply with "Hexagons tessellate and are more space saving compared to squares!" I'd like you to consider 2 things.
1) Why is the majority of our media in rectangular shapes? (hint: X and Y axis make it easy to isolate coordinates)
2) What is the simplest mathematical formula to describe a hexagon?