Here is a list of all pokemon that can learn Psychic:
http://www.serebii.net/attackdex/psychic.shtml
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Gardevoir is a psychic type of Pokémon in Pokémon Emerald version. To get one, you need to evolve a Kirlia.
Drowzee and Hypno are top choices. but most psychic Pokemon know/can learn Hypnosis.
Lugia can't learn psychic on its own, but you can teach it through TM29.
No.
It can't learn Psychic.