While probably not technically correct, and maybe not always the case. A simple way to think about it is that film is infinite resolution, this is because it is analog and not digital. Meaning the image on the film is not made up of a pre-defined number of pixels.
So as long as a copy is available on film you can always make a digital duplicate using the master film that will match whatever is the “best” format of the current time.
Whereas if the original is produced digitally you are basically limited to that resolution or lower without using some “artificial” up scaling of the digital master.
This is one of the reasons film is still used in industry, because it has archival value.
As far as over the air television looking better, this really depends on what you are comparing. Which may also depend on geographic location and services. And I might be out dated on this but at least in the US when they switched from analog to digital broadcasting, over the air was actually 1080p/i while cable was using 720p as HD. So broadcast at least at that time was actually better.
I assume cable also has some compression that is happening. But this may not be the case since cable boxes aren’t really a thing anymore. Unless TVs can just process the cable signal themselves now.
Doesn’t answer all your questions but hopefully points you in the right direction to look more into on your own if you’d like.