no
a pikachu
You cannot find Pikachu in the wild in Pokémon White, the only options you have in regards to getting Pikachu in Pokémon White is trading for a Pikachu, trading for Pichu and evolve it, defeat the Elite 4 and receive the National Dex and then access the Poké Transfer in Route 15 in order to transfer a Pichu (Pikachu's pre-evolved form) or Pikachu over to Black or White from Diamond, Pearl, Platinum, HeartGold or SoulSilver or you would also have the option to transfer a Pikachu from the Dream World over to White once the Dream World goes online.
You can import pokemon from your pokemon diamond, pearl, or platinum games via wireless transfer in which your DS connects wirelessly to your Wii and copies the pokemon in your storage and party so you can use them in battles in Pokemon Battle Revolution.
Pikachu's team
You can't find a wild Pikachu, Pichu or Raichu in pokémon Black and White. You have to transfer it from an other game.
No, it's a one way transfer. That way, you don't accidentally erase the Pokemon on your cartridge. However, you can buy gifts at the Battle Revolution store that you may receive through the Mystery Gift feature on your game cartridge. There are three Pokemon that may be received that way - Magmortar, Electivire, and Pikachu.
No, Mystery Gift Pokémon can be sent at any given time to Diamond, Pearl or Platinum as long as you have access to Mystery Gift and have a PokéDex.
You can't. You'll have to get one in Diamond, Pearl, Platinum, HeartGold, or SoulSilver and transfer it over to Black.
code
pikachu then pikachu evolves with a thunderstone to get raichu
Well, you could find a Pikachu in the trophy garden. You could find magnemite somewhere. but i would transfer a mareep from HGSS instead.
Lightball
If you transfer one yes. Pikachu are NOT wild Pokemon in Black and White.
transfer from diamond pearl platinum HG SS
Thunderstone can be used on Pikachu and Eevee, it evolves Pikachu into a Raichu and Eevee into a Jolteon.
There is no place in Pokemon White where you can capture a Pikachu. The only ways are by evolving a Pichu (leveling it up when happiness is in max) or by using the Poke Transfer (requires National Dex) to transfer it from Diamond, Pearl, Platinum, HeartGold, or SoulSilver. Pichu is also not capturable in either Pokemon White or Black.
Pikachu does not evolve by level in any Pokémon game, including Pokémon Platinum. Pikachu evolves into Raichu when a Thunder Stone is used on it.