First, with magic so clearly divided (though quite rare), is it likely that most or even all religious and/or scientific worldviews in that world would be based around six elements?
Scientific, yes. Religious, why? Divisions in religious thought often don't relate to how the world outside of human control is split up. They more often relate to good/evil, or human/spirit, or . . . well, you get the idea. Religions don't usually function in the same way as science does.
On the second question: I agree with sarah_frost. No nation is going to foreswear a weapon that will otherwise give the enemies a decisive advantage in war, or else it's going to lose that war. The only way I can see your empire refusing to use other kinds of magic is if Light and Shadow by themselves are so powerful that the empire believes it can win without resorting to the other types of magic. Rules of engagement and chivalry are usually kept only as long as both sides follow them.