Radiation is one of my favorite elements of the Fallout series of game. It can present a wonderful environmental hazard of course and is the source of many wonders and dangers of the wasteland. Without radiation we wouldn't have things like radroaches, radscorpions and the like to torment us!
Radiation and the Environment: There should definitely be regions of the world in FOOL that have permanent radiation environmental effects. Unless you want to increase your rad count a lot in these areas, suitable protection and treatments will be necessary. Heck there should even be some areas that have lethal levels of radiation exposure, nearly requiring protection of some kind lest you suffer some horrible fate.
Naturally there should also be the possibility of temporary radiation effects in the environment. These could be generated by weapon effects, in-game events, objects, various creatures and so forth. These types of effects should linger for a certain duration before expiring.
Radiation and NPCs: If players are to be subject to the dangers of radiation, so too should creatures, NPCs and all MOBs. Naturally those entities with radiation resistance will have a better time dealing with these types of hazard, no less would be expected. However should some foolish otherwise normal human raider follow you into a lethal radiation zone, I would expect them to drop dead after a short time. Of course, depending on the sophistication of the AI or scripting, such entities may instead run the other way for fear of over-exposure.
Radiation and Weapons: Certain types of weapons should generate radiation as a side effect of their use. However I also think there should be some weapons that exist for the specific purpose of generating radiation spikes in order to cause lasting problems for ones enemies. In a world with so much fear of a thing, it would only be a matter of time IMO till folk capitalized on this notion in order to produce weapons to generate such effects.