He Karen.
So you found an egg, cool. Are you sure it was laid today? I ask because if it's just dirty because she was all afluster, then it will be an okay egg. If you are not sure how long it was there, i usually toss them.
About cleaning eggs. I don't. Unless they are extremely dirty, then I'll just feed them to the dogs, but for my customers, I don't wash- to keep the bloom on them. i also leave them on the counter until sold, as I have very little room in the refrigerator. You can keep natural eggs with the bloom on the counter for almost four weeks. The stores wash their eggs, so their is no natural protection, which is why we must refrigerate those store bought eggs. This is the way I do it. There will be several responses on other's methods.
The hen may use the box, but she's new at this and shouldn't be bothered at first. Later, once she's used to squirting out those giant things, you can bother them all you want.
Yes, the eggs will get bigger.
Good Luck!
Lynn