Need to add elevator downforce to total lift when sizing wing area?
No.

First, your horizontal tail will need some control margin. A trimmed state where it flies close to c$_{l_{min}}$ is a grave design error. Next, your horizontal tail sees the same angle of attack change as the wing, reduced by downwash. This means that the strongest downforce is trimmed in fast flight, when the angle of attack is small. Fly slower and angle of attack rises not only on the wing, but also on the tail. Chances are that your tail produces positive lift in slow flight.

Flaps will change this picture slightly. Setting flaps will need you to re-trim the aircraft because now the center of the wing's lift has moved slightly backwards, so the load on the tail becomes more negative.

Fun fact: If you have a symmetrical wing airfoil, the trimmed tail load will be constant over the whole envelope. In order to achieve the best control power, this tail load should ideally be zero.

Now for the tandem wing: You assume that now both surfaces create lift, so overall drag should be lowest. But adding area on the tail will reduce the needed wing area. Given that the planform shape stays constant, less area means less wing span. However, induced drag is proportional to the span loading, and a lower span will mean more induced drag. Therefore, a conventional design with an unloaded tail of minimum size will have the lowest drag.