I'm not sure about the expiration date, but in my family we make like five dozen painted eggs every Easter and keep them in there for a few weeks and they don't go bad, never had a problem with them. We try to eat them fast but it takes a few weeks, even with 9 people.
Cooked eggs will keep for a long time. I cook about 5 or 6 at a time, then put them in the refrigerator and eat them for snacks. Sometimes they are there for a couple of weeks, even more. Have never had a problem. Never.