I think your questions have been answered. I'll add a bit of explanation about the temperature of wash water and why it is important. The egg has an air sac in it. If you wash an egg in water cooler than the egg, the egg and the air in the air sac cools off. When the air cools off, it shrinks in volume. This creates a suction through the porous egg shell and it pulls water into the egg. The water can carry bacteria with it.
If the water is warmer than the egg, the air in the air sac expands, creating a pressure in the egg and keeping any water from coming in through the shell. The recommendation is to have the wash water about 10 degrees warmer than the egg and you will be OK.
Hope this helps.