We don't wash but simply rinse our eggs if they visually 'look' dirty. They stay on the counter until used and if we are not keeping up with the girls production we put them in a carton once there is a dozen, and the carton goes in the frig and numbered to keep the rotation. As far as your hard shell problem, try cracking them on a blunt surface like the flat surface of the kitchen counter...if your not washing or rinsing as they come in, ALWAYS wash them before cracking! No reason to have chicken fecal matter in your food.
No fecal matter is deposited on an egg during the laying process. I know, I thought the same thing! There is only one vent, and everything passes through it, right? Poop, urine, eggs.... but I found out recently that when an egg is laid, the opening to the intestines is completely closed off internally. I know @aart has a wonderful video that shows egg development, it may show how the egg exits the body. I wouldn't mind seeing it again, if she would be so kind?