found this information abotu 3 speed hubs from Sheldon:

"When you remove and re-install a 3-speed rear wheel, pay particular attention to the axle washers. The axles are flatted, and there are special anti-rotation washers keyed to the flats on the axles. These washers have tabs that must face into the drop-outs to help keep the axle from twisting under load. The axle nuts are easy to strip because of the interrupted threads on the flatted axle, so you should lubricate them with medium-to heavy oil or grease. They do have to be tightened quite securely."

could the same regarding coaster brakes be true?

since this is a peugeot road frame would it help to use the spring loaded adjustment screws or that little insert in the dropout that is so common on older frames, especially peugeots. here on the left dropout.