Crystal probably polishes herself to maximise the reflective qualities of her shield against lasers and the such. The shininess quality is probably just a pleasant side effect.
While the Vita version of Nuclear Throne crashes frequently (especially if you die in the old ruins) this makes sense. The reason why the I.D.P.D is chasing you so vehemently is because of your messing with alternate timelines. When the game crashes, the entire timeline you're currently traveling through has just collapsed into a singularity.
Since Melting's skeleton is exposed, radiation probably has an easier time getting inside his body for mutation, which could explain his ability to get more rads.
How can Robot level up with rads even though it's not a mutant (or even a living being, for that matter)? It's nuclear-powered.
When you open the purple portal early with Horror's ultimate mutation, everything in the level dies instantly. How far does this effect travel? Does it limit itself to the level, or does it spread to the entire planet? Or even to the entire universe you just left behind? No wonder the I.D.P.D wants you dead so badly.
The I.D.P.D suddenly become mutated freaks after the third loop. All of said I.D.P.D arrive through portals like the previous ones did. What happens when you go through a portal with enough rads? You mutate.
