How to you pre-bake coca (pizza)

For your missing equipment, calibration, and control, you will have to substitute vigilance and technique.

Basically, if you parbake your crust, you should get something good.

Turn on your oven, probably as hot as it'll go. Unless you have a thick crust and a very intense oven, it'll be hard to get too hot.

1. Roll out your dough into a baking pan/cooking sheet/pizza pan.
2. Bake in the oven until the dough is just starting to brown.
3. Take it out, add toppings to the more-cooked side of the crust (flipping the crust, if necessary). Put it back in until the cheese starts to brown.

The process above is the lazy-man's method, and it works with my oven at 350F or at 500F or out on the grill at 750F and all points in between.

The "ideal" pizza that is the target of most pizza aficionados may well be beyond your reach. However, I make pizza a couple times a week, and most nights I don't worry about that. Delicious toppings on good bread and excellent cheese is a great meal, whether or not it matches stereotyped image of "pizza".

P.S. If you do get some equipment, get the pizza stone and put the crust directly on it (w/ or w/o parchment paper). Your crust will be crisper. In a pan, sometimes your crust may seem closer to bread than to pizza.

For a deep-dish pizza, around 425°F is right, and so is 20–30 minutes. That's starting with cold dough (need to keep the butter layers chilled, at least for a Chicago-style pizza).

Cooking in an aluminum 3" deep cake pan is fine. I suppose cast iron should work too (though it'll heat slower, so might take longer). As has been pointed out in comments, the cast iron much greater heat capacity may be part of the problem; I'd guess preheating it would help. (You can just put the cast iron skillet in the oven as the oven heats, though depending on how long you let the oven heat, you may want it in for only part of the time—no idea what the optimal temperature for it is). Make sure to have plenty of oil under the dough, and also cook on a lower oven rack.

I'd guess that you're using too-watery toppings. The tomato sauce should be pretty thick, much thicker than you'd ever use on a thin-crust pizza. Vegetables may need sweating to get some moisture out. If nothing else works, partially cook the crust (say, ten minutes or so) and then add the sauce and toppings.

I can vouch by Cook's Illustrated's Chicago-Style Deep Dish Pizza recipe. Normally they have a paywall, but currently that recipe isn't behind it, so grab it quick.