No, Mew is a legendary Pokémon and legendaries don't produce eggs. There is one exception however, Manaphy produces an egg, but this egg leads to Phione, not Manaphy and Phione doesn't evolve.
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It takes about 80,000 steps for the bad mew egg to hatch.
It's weird. Mew is said to be the ancestor of all Pokemon, but there is a myth that refers to the one who created Pokemon as "the original one", but that is actually arceus. How magby is the live coal Pokemon and gyarados is the atrocious Pokemon, arceus is the god Pokemon. It says the original one hatched from an egg, but pretend he is a chicken. Who came first, the chicken or the egg? In this case, the egg. But something had to lay the egg. I'm guessing mew. You can stop pretending arceus is a chicken. One other option is that since mew is said to be the ancestor of all Pokemon, it's possible to doubt. The only proof is that mew can use transform to copy any move, metronome to automatically use any random move, and it can learn every TM and HM. I hope this helped...
Mew can be migrated from Pokemon Emerald if that game was participated in the Japanese Mew event to get the Old Sea Map or have 999 Pokemon in Pokemon Ranch and Hailey will give you Mew.
No, you cannot get mew in Pokemon white or black
Mew is a Psychic-type legendary Pokemon.