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
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
Haven't heard that one before. ROFL! Uh, are you sure you got the right words there? I don't know about you but I'm sure there isn't a TM with that.