Welcome @Abigaillynn!
1. A "free" Eevee is in Celadon, you must beat the Team Rocket there and free it from the machine. Also, once you see an Eevee in a battle you will get Pokedex data, so you can use that to check out every location possible to find your own one.
2. As far as I know nobody can use Items apart from Held Items in PVP battles. (To make your Pokemon hold items just Drag and Drop. Remember they can only use Berries and Held Items, like Leftovers, or Oran Berry, but they can't use Potions or Ether's... etc)
3. Remember to battle Pokemon around the level of yours, since you are new, I recommend you to only battle Pokemon a bit lower level than yours, and the first 15 levels it is easier to just attack every turn.