i will say about the mons that give high coin immediatly after entering habitat, it does look like it gives you cash if you have had them for a time, as if its secretly collecting coin unobtainable at least till you put them into habitat.
for the breeding it says in the small text when you first pop in that thier the egg made will have a random trait, so by that logic it should not matter what traits the breeding pair have, since otherwise it'd make more sense for it to say otherwise