Regarding bit-depth: 8 bit per color channel gives you 256 levels of each color, since one bit is either 0 or one. Leading to a total of 16 million possible colors, and there are three color channels, so that's 24 bit. 32 bit gives you one extra channel, which is used as an alpha (transparency).
Regarding color issues: When I have those kind of problems, it's usually because something goes wrong with color-spaces and/or profiles. Like program X saves the image in sRGB, but program Y knows nothing about ICC profiles, yadayada... This is messy stuff. :cry: