Hardware sprites are paletted with either 4bit (16 (16bit) colours, 16 different palettes) or 8bit (256 (16bit) colours, one palette at a time)
There are three 'bitmap' background video modes:
Modes 3 & 5 have 16bit colour.
Mode 4 has a 8bit palette with 256 (16bit) colours.
There are four tiled backgrounds, various of which are availlable depending on whether you use Mode 0, 1, or 2:
I think backgrounds 0 and 1 can use:
32bit colour;
8bit with a 256 (16bit) colour palette;
4bit with a 16 (16bit) colour palette;
I don't think tiled backgrounds 2 and 3 can use 32bit colour. I'm not that sure, though.
The GBA has no OS and no file formats, so it doesn't use PNGs. If you look into GBA programming, (seriously, don't), then you end up #including endless C arrays.
As for the programes they used, who knows ^_^ Could have been anything, even something they specifically produced.
Btw, the GBA is a 32bit machine.