As long as you keep it casual you should have no problems selling eggs to friends or neighbors.
You can not, however, sell them at a farmers market or similar venue, the health dept. will get ya.....unless, of course, you do it "under the table" so to speak and advise your customers to keep it hush hush you should be able to do that but, you must have another reason to be at the farmers market and not just show up with eggs only.
What we do is just have a small group of friends who readily buy eggs from us for $2 a dozen and will call us when they need some. It really just covers the cost of feed and is a good way to recapture your expenses.
As far as cartons, just have your friends save theirs for you. You need not have new cartons. If you have a lot of chickens, you can find "seconds" in most places that sell cartons, these are inexpensive and work just fine.
Don't bother washing eggs...the natural "bloom" protects them from spoilage....if you get dirty ones, just use a light sandpaper to clean the dirt off.