Dogged Detective doesn't need to be in the graveyard when the first card is drawn for its last ability to trigger. As long as it is in the graveyard when an opponent draws their second card in a turn, it will trigger.

When you surveil, you may put all the cards you look at back on top of your library, you may put all of those cards into your graveyard, or you may put some of those cards on top and the rest of them into your graveyard.