If you are really concerned about bees dying from Permetyhrin poisoning remember that it is the active ingredient found in Marigold Flowers or other flowers in the same family. It is also a powerful insect repellant and if used according to instructions any honey bee deaths will be minimal...
A liquid is the best way to treat for mites and lice. A liquid spray or perhaps a 50% wet able powder sprayed on and into every last nook and cranny in your chicken house will work wonders, especially for Red Mites.
I have always been partial to painting the roosts with used motor oil to deny...
I don't know if bathing a chicken is harmful or not, I certainly would expect a bath to remove part of the mite load, but I can not see any true benefit if one must still use a pesticide afterward to control mites. I do know that if you bathe a duck in detergent that it sinks instead of swims...
Your first conclusion is correct.
Everything works to prevent mites as long as your chickens are mite free.
Your third conclusion is also correct.
Free range chickens will always get re-infested with free range mites that are picked up from wild birds sharing the chickens environment...