Definitely look forward, not straight down, although I have a habit of concentrating on road debris in front of my bike.

I used to ride in the drops a lot. Not so much now. But, depending on how you hold the bars, riding holding on the tops of the hoods, with the forearms resting across the bars parallel to the ground may not be so different from riding in the drops with straighter arms. It might also be good practice for lowering one's body.