Since getting unhappy girl early is very important in farm decks, using Rai-Mei will essentially make it feel like you have 6 unhappy girls in your deck. It's also useful for deck thinning by attacking into your opponent's monster if they have higher attack.
You can use Blue Dragon Summoner to the arms and legs.
Magician's Circle to the head, and it's up to you to find a way to sent this back to your hand (maybe Monster Reincarnation?).
Also, all Exodia pieces are spellcaster type. Now... good luck.
No. Actually, there's a similar cards, but a searcher for level 1 or 2 machine, warrior, dragon, aqua, spellcaster, or normal monster. you can see the details here: http://yugioh.wikia.com/wiki/Searcher