If this is the case, you're playing Pokemon Yellow. Yellow prevents the starter Pikachu from evolving due to following the anime, where Pikachu refuses to evolve (though it's possible to evolve it by trading it to another game, evolving it there, and trading it back to Yellow).
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Pikachu do not evolve by level. They evolve when a thunderstone is used on them.
Pikachu will evolve into Raichu when given a thunder stone. If you mean Ash's Pikachu, then it very unlikely he will evolve his Pikachu, as Pikachu is the Pokemon Franchise's mascot.
Yes. When Pikachu has enough happiness, level it up then it should evolve. Then you can evolve Pikachu by using the Thunderstone to evolve Pikachu too Rachui. Remember: Rachui CAN NOT EVOLVE.
No, sorry
Pikachu does not evolve through level-up -- instead, you can use a Thunderstone for it to evolve.