all radioactive material decays at the rate of it's radioactive half-life.

Half of the material decays at the end of the half-life. Not all of it. So it's always halved over and over and over, every time a half-life's worth of time passes.

Decay involves the splitting of unstable atomic nuclei, which produces both EM and subatomic particle radiation.

Correct, I agree with this and everything after it, it's factually correct as far as I understand.

I'm not sure what prevented the radiation from damaging the film, but that's a separate topic.

The signal was damaged. Just not enough to ruin it. And there was no film, they were piping the images from the robot to the place where they were controlling it, so that's why they got the pictures. It's like a live TV stream from the robot. But the information stream was still damaged by the radiation before the robot shut down and stopped transmitting.

It's difficult for me to imagine how a person could avoid receiving deadly doses of radiation when handling 14 lbs of weapons grade plutonium with shims, and screwdrivers, and thumb holes, etc.

Because it's not supercritical. The elephants foot is supercritical. This means that the reaction is happening in a runaway fashion, and is impossible to stop.

The demon core was sub-critical. To make it go supercritical, you have to enclose it in a neutron reflector shield, in order to make enough of the neutrons bounce back to hit the demon core, to make it go runaway. This is how the device is detonated, essentially, by ramming the two neutron reflector halves around the demon core, so it's completely enclosed and that creates a runaway reaction because of all the neutrons reflected.

Onlookers watching over shoulders, etc.??? I think it's safe to assume that shielding wasn't used, if they were using shims, and screwdrivers, and thumb holes.

Yes, it's super unsafe practice that would never be allowed today, but at a distance from a sub-critical mass, the radiation received is not fatal or even really dangerous. The CIA has been known to dose people with plutonium to induce cancer, but it literally takes years before the cancer sets in, and that's after the plutonium is ingested!

There's not just "radioactive" and "non-radioactive", there is a wide variety of rates of radioactivity. The elephants foot was extremely extremely radioactive, because it was in a supercritical state, meaning neutrons were flying and atoms breaking down actively, and it was going faster and faster.

Whereas the demon core was sub-critical, meaning the reaction would go slower and slower if left alone. A small piece of plutonium emits radiation, but when it's not being bombarded by neutrons, it is not nearly as radioactive, because it's not generating neutrons and undergoing atomic breakdown nearly as fast. Closing the neutron-reflective shell around it creates enough reflected neutrons that it begins to runaway, which is what happened when he accidentally pulled the screwdriver out. Then the two halves completely closed, and the plutonium went critical, which also means the amount of heat and radiation it outputs goes up a million-fold in a matter of microseconds.

So it's important to understand that when a nuclear reaction is in a runaway or supercritical state, it produces much much much more radiation than when it's sub-critical and just sitting there decaying naturally at a much slower rate.

Or the movie was made before the propaganda was.