Its better not to wash the eggs because you will wash off the bloom that creates a protective barrier. And no, they don't need to be refrigerated. Because grocery stores keep them in the dairy section, many people believe eggs are dairy and need refrigeration but they will last for quite a long time kept at room temperature.
no you do not need to wash them, if you are going to sell your eggs you would do best to refrigerate them. Hi, from Big Bear Calif, always good to meet another feather brainier.