I pick up our eggs daily from the nestboxes - but if they've been out a couple of days, the only danger is that a hen may go broody and want to sit the nest. The eggs will keep out there - even in warm weather, at least several days. Any longer than that and they are at risk of getting cracked, broken, eaten or sending a hen into a broody state.
I do not wash the eggs unless they are dirty as they are protected by the natural antibacterial "bloom". I keep my eggs indoors on the counter until used - usually no longer than a week.
If I do wash the bloom off an egg, I will either use it right away (within a day or so) or refrigerate it. Refrigerated, the eggs will keep several months, but who wants to keep eggs that long anyway?
When I do wash eggs, I just wash them with water and dry with paper towels. But as I keep the nest boxes clean, my eggs are usually clean. Sometimes a floor egg will be dirty - then I wash it it, dry it and use it right away. After all, I don't eat the shells...!
Kate