Yes, I can answer all those questions.
First, don't just get an oven. Find one that will get to and maintain 400 degrees. I personally have had great success with the Hamilton Beach Countertop Convection Ovens. I have two, one I had already and the other I found, which appeared unused, at a Goodwill Store for $20. I can cook 1200 to 1500 bullets at a time in either of my HB ovens.
I have a Black & Decker toaster oven that is junk, it will get to temp really fast then wanders about 50 degrees. I also have a 30" digital wall oven I got for free because the control panel was shot and it would cost a bunch to replace. For about $75 I installed a PID and converted it into a PC oven for larger projects. It will get to 400 degrees quickly and hold a constant temp within 2 degrees. I use it to coat parts, tools, artwork, etc. and I guess if I wanted to do 10K or more bullets at a time I could use it, but the HB ovens are really all I need for bullets.
Depending on the process used, the powder and the humidity the thickness of the coating can vary, but usually between 1.5-3 mils. Preheating will definitely increase the coating thickness.
You can size before PC, but you are still moving metal. Some do this to try acheive a better formed rifle bullet. For handguns, sizing before PC in my opinion would be a waste of time and effort and more likely to contaminate the process.
You can use gas checks and PC together. Gas checks on PC handgun bullets are a waste of time effort and money. If the bullet is a proper fit for the barrel it is already sealed and if it is powder coated the coating can withstand the temperature and will have no gas cutting. Gas checks are not needed at all on a PC bullet, but a GC can provide a flat base for the bullet, which enhances accuracy. A properly coated & cured PC bullet will resist the tork of spin out and I have personally fired PC bullets exceeding 3500 FPS with no leading. At handgun velocities you can coat pure lead and have no leading.
I personally have been PC since 2012. None of this requires experimentation as that has already been done by me and numerous others who PC.
It looks to me like we already have the hook in your mouth, so all we need is a quick yank to set it.