I completed the emerald nightmare on heroic and mythic difficulty, but not a single boss dropped CORRUPTED ESSENCE (required item for the quest Emerald Nightmare: Essence of Power). Since the quest said I can complete it in normal or higher modes. Is this a bug, am I out of luck or did I do something wrong?
you only get one chance for it to drop per boss, no matter the difficulty. If you clear it on heroic, you wont get any more drops by doing it on mythic or normal after. For your situation, did you clear it on normal before you had the quest? If so, that clear counts towards your weekly chance for the drops, so you will have to wait until next week.