My main question is, can I just put my chicago in the pan on pre-heated stone? Will it still cook okay and not burn?
My 2 cents:
Many of us recommend
baking your deep dish on a preheated stone, so it's not a problem.
As for adjustments, that really depends on your oven.
In general, if you're getting good results without the stone, you'll probably want to pull your deep dish out 5 minutes early (or more) when using a stone to avoid over-baking the bottom. The only way to know how long is to try it once in your oven and see how much your oven varies using a stone.
I don't know what size pizza your baking, but my deep dish 12" pizzas usually take 30-40 minutes to bake at about 460.
I say this a lot in my posts, but I often use a sheet of heavy duty aluminum foil on the top rack to shield the top of the pizza.
On the rare occasion when I make thin crust, I usually crank the oven up to 500 if I'm baking directly on the stone.