For the drag chains:
My old machine had drag chains down both sides. On one side I ran the signal cables and on the other side I ran the stepper cables and power lines (pump, light etc.). This was to keep them separate for interference. I've seen others groups them all together so maybe not required but it would give you double the space. Each one was quite large if I remember correctly, maybe 50x20 or so?

For the cooling:
An earlier version of my old machine had the radiator on Z axis and that worked fine but did not look very nice with all the tubing sticking out. I moved it to the end of the gantry which was better.
On my next machine I'm planning to run the cooling pipes all the way through the drag chains and off the machine to a reservoir tank (no radiator) as I found the spindle got barely warm even with the fan off (and sometime the pump off as well for small jobs). I will rely on the thermal inertia of a much bigger tank of water. Easy to add further cooling if it does not work but experience of the old machine suggests it will be OK.

Compressors:
I'm no compressor expert but when I last looked at them you could either have quiet and low flow rate, or noisy and high flow rate. If you wanted higher flow and reasonable noise you needed to get multiple cylinders, belt drive but they were a lot more money.