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What you would see is clusters of tiny whitish eggs at the base of the feathers, or tiny bugs moving on the skin or along the feathers.
Lice and mites are almost unavoidable, one of those things that are best handled with a prevention program. They are carried by wild birds. Frankly, the simplest thing would be to pick up a can of "poultry dust" at the feed store and dust them: on the neck, around the vent, and under the wings, particularly. Even if this is not the root of the problem, it won't hurt, and they probably could use the treatment. Poultry dust is usually perethrin and/or pyrethrin, not exactly highly toxic chemicals.
No, you won't necessarily see redness, swelling or irritation. Depends on the cause. Not necessarily present even with mites/lice.
It could be that the root cause of the problem is feather plucking. This usually happens because of protein deficiency (feathers are high in protein.) Simple enough to increase the protein in the diet: just add a little as a treat. Yogurt, meat scraps, a can of canned mackerel, fish scraps from cleaning fish, cooked egg, table leftovers with meat in them -- whatever is handy.
Protein isn't typically cheap, so I am always a little suspicious that standard chicken diets might be a little low in it.