How long do they last at room temp? Does sliced vs unsliced make a difference?
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I would keep Them unpeeled. And after 12 hours don't eat them
2 hours, same as any potentially hazardous food. Slicing increases the exposed surface area proportionally increasing risk of contamination -- but the recommended 2-hour limit will keep any bacterial growth under safe limits.
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Just a couple of hours according to FDA and USDA. Given that short period, slice v. unsliced shouldn't matter too much. (Raw eggs can last a lot longer than hard-boiled ones.)
Although NOBODY would recommend this, 50 or so years ago we would have hard boiled Easter eggs in a bowl at room temp for a week. Nobody ever got sick.