What -exactly- do the various transformations do to the projection matrix?

What effects do transforming the projection matrix have?

i’ve seen translations performed on it, why?

Transforming the projection matrix is the same as transforming the modelview matrix, or at least the polygons is projected on the screen the same way. However, you should never EVER use the projection matrix for doing translations. This will mess up a number of things, like lightning, fog, sphere mapping, and maybe a few more things.