Deoxys can learn Psycho Boost
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No, Mewtwo cannot.
All Pokemon with a water-type can learn it. There are some other Pokemon that can learn it, but mostly water-Pokemon.
I don't know all of the Pokemon that can learn Headbutt, but I know that Cubone can learn it.
Any Pokemon that can learn a electric move
You have to eat a lot of Gummis and watch your IQ boost. P.S. Find your Pokemon's favorite Gummi to make its IQ boost faster.