There are no stupid questions, don't worry!
Inside the coop, D.E. can be useful if you get it well down into the joins of the sides, and into the perch ends, and also all around the edges if the nestboxes. These are the places where redmite will hide away at night. Unless you have a really bad infestation they won't be so likely to colonise other more open flat areas, so go for treating the nooks and crannies first. Some people make the DE into a slurry with water and paint it into cracks then let it dry out.
As you say, DE can be dangerous stuff if breathed in, and this applies to the chickens as well as humans. Personally I don't spread masses of it into the bedding for this reason, as I don't think its good for the girls to be breathing it in an enclosed space. I also don't see any advantage in feeding it to the birds. There are lots of chicken tonics on the market, mostly quite unnecessary if your birds are properly fed and in good health anyway, and a regular worming programme with Flubenvet is all that is needed in a routine basis. But the stuff from the farm shop is fine, I expect its just the same as the more expensive version in little packets and will last a long time if kept dry. Or you can use redmite powder, which I suppose is DE with added insecticide to actively treat the mites. I use this, to make the smaller quantities more effective. It also smells nice.
I think its important to check regularly to ensure any outbreak of redmite is detected immediately, then you have some chance of dealing with it before it gets out of hand. But there's no need to get paranoid, many people, myself included so far, never get redmite, (famous last words, I know!) especially if you have a plastic coop and keep it clean, within an enclosed run that wild birds have no access to.
