None of the depicted particles is radioactive. They are just the product of radioactive decay. And btw, neutrinos are also the product of radioactive decay, they just interact so little with anything that we can't effectively measure them from radioactive substances. (We can measure them from the sun though.)
Huh. TIL neutron radiation is more penetrative than gamma radiation. I would not have expected that, since neutrons have mass and volume and photons don't.
Googling tells me they'd both have approximately the same wavelengths (depending on the speed of the neutron), so I guess it's probably that gamma rays would interact more strongly with electrons?
It's about which forces act on them. Other than neutrons, every particle here will interact with charged particles (e.g. electrons or protons), which makes it an EM interaction. In the world of particles, EM is long range. Whereas the force that acts on neutrons is very, very short range. There's no actual touch the way we think of it, outside exotic conditions like in supernovae. Think of the size of a nucleus vs an atom. Those are the two forces keeping them together.
The way concrete stops neutrons is similar to a pinball machine. It doesn't need to be a solid material, it just needs to be dense. It just so happens that solid materials tend to be denser. But for example, older nuclear reactor designs use water to slow the neutrons.
Btw this is a very clever use of water and by no means dinosaur tech. We just have more clever materials now, e.g. molten salt.