Yes, they can. But Pokémon gain experience points much slower, even if they battle one another. The first evolution would be at the earliest timing of month from acquiring the pokemon. The second evolution phase a little longer, but only like a weeks longer or so (so 5 weeks from evolving the first time).

As for stone evolutions for Pikachu/Eevee, there may be some misc. vending machines with some peculiar looking stones in them.