Layer feed is normally 16-17% protein. Some people feed lower protein scratch or grains that may be more like 8%. That type of feather picking is fairly common. I have one or two that look like that even though they are outside roaming all day, have their bottoms sprayed, and get layer...
That looks like feather picking to me. I don't know of any egg withdrawal with Permethrin. But I would not use lice or mite treatments anymore unless I could actually see any bugs or evidence of them. Feather picking can occur if they are over crowded or not being let outside to roam first thing...