Well, for item 1, I wouldn't use any detergent. A water rinse wouldn't hurt. I don't know how the bees would react to the perfumes in dish soap. (just my uninformed opinion)
2.... That is a mystery to me.
and 3.... Fortunately I haven't had the "pleasure" of dealing with a laying worker hive. When I've discovered queenless hives, I steal a frame of fresh eggs and open brood (making sure I don't accidentally steal the queen with it) and transplant that (with nurse bees) into the queenless hive. They will either raise a queen or dwindle away. So far, that's all I've had to do.\
Your mileage will vary.