Charles (ckreef) is the Pro here for all things pizza. So look for some of his pizza cook threads and dough recipes. There are others here that are wise, as well.
I'm no expert, but can offer a couple of tips.
First, most important, heat soak your grill for at least an hour once you reach your desired cooking temp. That stone takes a long time to heat up to match the dome thermometer temp. If you have an IR heat gun, use it to check the stone temp to ensure it's at the cooking temp you want. Also, when using the KK stone on the upper grate, there's no need for an intermediate heat deflector - it just slows down the heat-up process. It can handle the direct heating.
Cooking temp depends on the style of crust and dough recipe - hence, the reason you're seeing the big range. Really hot temps (>550F are for Neopolitan style). Most regular style pizza cooks just fine at 450 - 500F. Deep dish styles do best at lower temps 350 - 375F.
Cook times also vary with style and dough recipe - really thin crusts at high temps will be done in a matter of a couple of minutes, which is why it's essential to cook up near the dome to get the top done at the same time as the bottom. Regular styles take around 8 - 12 minutes. Deep dish go for 30 - 45 minutes.
Parchment paper - my go to for getting the pie off the peel onto the stone. It barely affects the browning of the bottom crust; but if it bothers you, wait about a minute then, you can slide the peel between the crust and parchment and easily remove it once the crust starts to brown. I like it because it works, first of all; and second, you don't get any scorched flour or cornstarch flavor on your pizza.