It really depends on the production - some of them, particularly animated ones, had to develop their whole pipelines from scratch as part of their early productions. You can bet that time was accounted for as part of production costs. Same for pioneer productions like The Mandalorian (iirc costing $3m per episode, a large chunk of which went into developing experimental 3d soundstages).

For the more common endeavours, then no, of course - they just use what is there, or more likely outsource it to specialised providers in the same way as they would outsource e.g. building a website.

Paying money for a tool means having a person develop that tool for you.

Obviously yes, but if you're attempting to add up person hours worked for some project, I don't think you would include the hours spent in say Mac OS.

Sure, but game devs use tools like unreal engine the development time of which shouldn't be factored into the human hours calculation