Both untrue. "BAD EGG" is listed when an invalid Pok?mon is in the roster. This usually happens when you mess up a Shark code, but game bugs can cause it from time to time. They acts in the game like normal eggs, but the Pok?mon type is BAD EGG instead of EGG, and they never hatch. There's nothing sinister; it's a simple placeholder like Missingno, but made to be totally stable and not do anything.