The problem we are having is that the specific BRANDS of dusts and gutloads make a difference because of their ingredients. If your cham's jaw is deforming since you've had him there IS something wrong with what you are feeding him or exposing him to. Sounds like the Zilla light isn't producing enough UVB in the right spectrum, or the dusts are either old, deficient, or not balanced correctly. You need BOTH vitamin and mineral dusts. Baby chams grow extremely fast, so deficiencies can very well show up in a month if he can't metabolize Vit D and calcium. You can correct this. I'd really suggest getting a ReptiSun 5.0 fluoresent tube bulb, getting him out in real unfiltered sunlight whenever the weather permits, add some fortified cereal grains (like Total) and orange chunks to your gutload (vit. C and the dietary calcium will help), get a decent calcium dust (ReptiCal or MinerAll are good), and a vitamin dust like Herptivite. He should be getting a light calcium dusting every day, vitamins once a week until he's about 8 months old.
It sounds like the black spots are bits of old shed. Just watch to see if any new ones keep forming.
As for the eye, I suspect your setup is too dry. 55% is pretty low for a baby cham. If you add a live potted plant instead of twigs and fake leaves it will provide a lot more surface for water retention and drinking, give him a hiding area, and help stabilize the humidity without drowning him in the small tank.