The reason Inferno magic was even put in was because apon creating my character I kept pointing out to Lucius how I could abuse it. (and others could.) Not having it or simply baring demonmancers from summoning demons that can use other elements would nerf them quite a bit. The Inferno magics were designed to be different from the normal magics because they were more limited and specific in scope to all the mage bloods.(not to mention Baulder couldn't exist) So removing it would be a horrid idea as it would either by proxy buff or nerf Demonmancy quite a bit.

Though I agree with Noxomancy needing to be retooled, it honestly seems borderline useless right now. I like the idea of plague crafting but they need something else to do as they arn't terribly useful in combat (unless your a master) and only really seems suited to be used by a big bad mage blood.

Having Cyromancy and hydromancy taught at the same time to students would be a good buff for them as like you said their better together. Though it might seem weak do to a lack of creativity, because if you really wanted you could just rip Sub-zero's moves from Mortal Kombat and have a bad ass ice ninja. 

I honestly think Pyromancy and electromancy should  should both either merge with each other or the thing they accompany as they again are both useful in combat and not much outside of. Hell these problems might be fixed by allowing people to specialize in the school rather than either of them individually. (this would require that demonmancy and necromancy be split up though as OP.)