Elegant Egotist is a Yu-Gi-Oh trading card
No, Mewtwo cannot.
At level 100
MetronomeClefairy, Clefable, Mew, and Mewtwo can learn Metronome.
Nope, I just tried it.
Elegant Egotist is not a Pokemon move, so no.
If you have the TM for Elegant Egotist, than Mew can learn that move.
If that's a move then yes.
Elegant Egotist is a Yu-Gi-Oh trading card
In Pokémon, "Elegant Egotist" and "Double Team" are not the same move. "Double Team" is a status move that increases the user's evasion by creating illusory copies of the user, making it harder for opponents to hit. "Elegant Egotist," on the other hand, is a signature move of the Pokémon Zoroark, which has different effects and is not widely recognized in competitive play.
Mewtwo doesn't learn Psybeam.
No, Mewtwo cannot.
Mewtwo may only learn Shadow Ball by using a TM
This is a yugioh card...sorry to disappoint but harpy ladies don't exist in Pokemon and indeed have no spell support.
No, Mewtwo cannot learn Earthquake. It is a Psychic-type legendary Pokémon and Earthquake is a Ground-type move, which is not compatible with Mewtwo's movepool.
Train your mewtwo it will learn aura sphere at lv 90-100
At level 100