The only place to find an Eevee is at Bill's house or maybe at the GTS.
Get Eevee from bill in glenrod city or from the betting place. The train him in entana forest. He should evolve there.You can't, except by trading an Eevee to D/P/Pt, evolving it to Leafeon in Eterna forest and trading it back to HeartGold.
the elite 4
you can't...
it is a the top of the pokemon center
The best place to evolve a Pokemon in Pokemon Heart Gold is at Mt. Silver.
find a place that has wild Pokemon the same level as it.
Eevee is found in the same place as it is found in Diamond and Platinum. In the Pokemon Mansion by the route below Hearthome City.
you dont, its not in HeartGold or SoulSilver, Ho-oh (HeartGold) or Lugia (SoulSilver) take their place. You can also get mewtwo
The gs ball.
there is a event
You need an arceus.
grass