Do i understand correctly that post-processing effects like bloom are therefore forbidden? Or are graphical elements (images) only allowed to consist of these colors, while other effects like shading are still allowed?

As I understand, every single pixel in your game must be a color from the palette. Anti-aliasing, shading and post processing are all forbidden since they produce pixels of different colors.

e.g. say you’re only allowed to use black and white but you use anti-aliasing

see how anti-aliasing has created extra gray pixels that would not be allowed? The same goes for any other thing that creates pixels of different colors from the ones in the palette.

While I wouldn't use any post processing that produces radically different colors (lens flare, chromatic distortion) I wouldn't obsess over stuff like anti-aliasing and shading from shadows and light sources. You'll be spending too much time writing shaders (depending on your engine and game type).

I won't be rating games by checking every pixel. If the colors look vaguely right you're good to go in my book.