When you search the target's controller's graveyard, hand, and library, you may leave any cards with that name in the zones they're in. You don't have to exile them.

Deicide looks at the card in exile, not the permanent that was exiled, to determine if it is a God. For each of the Gods in the Theros block, it won't matter what your devotion to its color(s) was. The card is a God card when not on the battlefield.