I always do export as a .png. So you're saying for things like the eyes I should export as .tga? Maybe I'll try that next time, thanks.
Actually, it's only recommended to export texture parts as TarGA (.tga) images if they're in the IA4, IA8, RGB5A3, and RGBA8 formats, since those are the texture formats that utilize multiple transparent colors. Likewise, CI4 and CI8 textures that use IA8 and RGB5A3 palettes are fair game too.
However, you can still export textures as PNG images if they're in the I4, I8, and RGB565 formats, since those formats don't utilize transparency at all. This also applies to the CI4 and CI8 textures that use RGB565 palettes.
Lastly, CMPR textures only accept "1" transparent color, so you can export the CMPR textures as PNG images without any worries.