You said..."My veiled chameleons are starting to hatch in the incubator. This is all very new to me. Do I keep them in the incubator in the dark. Or do I put the container in which the are hatching, into the prepared enclosure?"... Neither.
Leave them in the incubator until they are fully out of the egg and moving around in the container you're incubating them in...then move me to a baby cage. You don't want to leave the lid off the container the eggs are in formverynlong when you open it to get the baby out because it will change the humidity and temperture and make it hard or impossible for the rest of the eggs to hatch. More about baby cages in a while..I have to look for sites for you.
You said..."Side note: how soon do I start hydrating them and feeding them?"...you will need pin head crickets or fruit flies to start off feedin them with. You can mist the plants in the cage to provide water...do not spray the babies directly. More about this in a few minutes too.