So to restate, you want to move everything from the DX to the single-speed's frame? Depends primarily on the head tube length and diameter.
You want disk/disc brake, which means the front fork will require caliper/calliper mounts. If the existing SS frame has mounts already then the existing fork could be okay. Otherwise you're up for moving the front fork over from the DX. If its the wrong diameter, the new fork won't fit in. If its the wrong taper, it won't fit in. If its the wrong length, it won't secure. So you may stay with the existing rim brakes, rim and wheel.
Swapping the transmission over requires the rear dropouts to be the same or very close to the same width. Otherwise the geared wheel will not seat properly and can move under load.
Your front cranks may be okay to swap for the double or triple chainring, but it depends on the bottom bracket connection being the same.
To be honest, this sounds like a frankenbike which will use up a lot of time and may be unpleasent to ride.