You have to beat the Elite 4 to get the National Pokedex. Then you go to Bebe and she will give you an Eevee.
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I'm not sure if you can catch Eevee in Pokemon pearl but you get it as a gift from Bebe in Hearthrome City after you get the national dex.
You can't catch Espion you must evolve it from an Eevee by using a moon stone on it to get an eevee go to Heathome city in the house next to it to get an eevee.
It takes AT LEAST 9180 steps to hatch an Eevee.
eevee does only evolve into glaceon in dimond, pearl, platinum ss and hg
I think eevee is a Pokemon that cannot breed. Have you checked that one is male and one is female?