No, you cannot do so in LeafGreen. While Eevee can normally evolve into Espeon and Umbreon without stones, the lack of a time system in the game prevents Eevee from evolving into one of them.
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No, Eevee does not evolve with a Shiny Stone. Only Togetic, Roselia, and Chillarmy evolve with it.
you cant evolve eevee with a moon stone
Eevee does not naturally evolve. If you want to evolve it you need either a water stone, a fire stone, or a thunder stone. To obtain these stones you can buy them in the Pokemart in Celadon City. With a water stone, Eevee will evolve into a Vaporeon (water type). With a fire stone, Eevee will evolve into a Flareon (fire type). With a thunder stone, Eevee will evolve into a Jolteon (electric type).
There is no stone needed to evolve (although i think it should evolve with sun stone) .But your friendship with the eevee has to be very good then and only then will it evolve into an espeon
To make Eevee evolve into a Flareon, you have to expose it to a Fire Stone.