ad 1. I guess that for turbojet aircraft thrust change according to airspeed can be disregarded. Thus, thrust available is reduced by thrust normally produced by inop. engine. Hence, speed for minimum drag Vmd is still an airspeed for maximum range.
ad 2. Firstly NADP2 is not a replacement, but a procedure intended to be executed when protecting noise sensitive areas that are located further away. The difference between NADP1 and 2 is the moment of flap retraction. In NADP1 the flaps are retracted not above 3000ft AGL (Thus may be lower). In NADP2 flaps are retracted simultaneously with thrust reduction at 800ft AGL.
ad 3. Increased V2 takeoff procedure allows us to extend ground roll on remaining distance of the runway when for example our t/o is climb limited but not field limited. Increased V2 has many advantages. Flaps are retracted faster because acceleration to Vzf takes less time. It results in increased climb gradient as well.