Ryan, I'll take a crack at this:
1. The chain is on the inside because the sprockets are screwed to the ends of the rolling pins. Since the rolling pins have internal bearings and ride on a shaft (which originally ran between the handles), torque has to be applied directly to the wooden body of the pin. The upper shaft is cranked because there's no other way to get power (through the plates) to the chain.
2. The photos in Reply #65 show that where the inner plates have a hole for the upper rolling pin shaft, the outer plates have a slot. On the bottom, the inner plates are slotted, and the side plates have holes for the lower shaft. When the rolling pins are in place, the shafts are constrained by the matching slots and can only move in a straight line, closer or farther apart.
3. Behind the round discs, the inner plates have another slot (and the outer plates have holes). The shaft passes through the disc off-center, so when the shaft is rotated, the disc "wobbles". The stop blocks visible in Reply #76, welded above and below the discs, convert that wobble into linear motion, forcing the rollers together or apart. The discs need to be 'timed' on the shaft, with Top Dead Center the same on both ends, or the rollers won't stay parallel.
4. (partial credit) The green arm is a tensioner for the chain. Tightening the bolt at upper right (and locking it in place) pushes the idler sprocket up and tightens the chain.
5. The green disc is a close-up of the ball detent that holds the rollers in place (against the pressure of the dough) until you move the thickness adjustment handle. I believe that the spoon taped to the handle of the locking pliers in Reply #78 is serving the same function
In Reply #82, it looks like there's a jam nut between the handle and the plates (just snugged) to hold the thickness until you change it.