I would love to know about some curious questions, for example: If there's a generally static scene with just characters walking through it, does the render take advantage of rendering the static parts for the whole scene once , and then overlay and recompute the small differences caused by the moving things in each individual sub frame? Or, alternatively what "class" of optimizations does something like that fall in…
Not any more. It used to be that frames were rendered in bits then composited to make the final image. However, you then need lots of tricks to reflect what would have happened to the background as a result of the foreground ... shadows, for instance. So now the entire scene is given to the renderer and the renderer is told to get on with it.
Regarding physics cheats, it depends on the renderer but basically none. AI despeckling is making a huge difference to render times, however.
Directors don't get involved in scaling laws and stuff like that. Basically a studio has a "look" that they'll quote around.
Compute relevant techniques? A renderer basically solves the rendering equation. https://en.wikipedia.org/wiki/Rendering_equation
And have a look at Mitsuba! http://rgl.epfl.ch/publications/NimierDavidVicini2019Mitsuba...