You will need this Complete Compact THC MD system ( CNC Plasma Z axis controller ) | eBay, or at least half of it, it works with both type plasmas. Look at the videos in You tube or their web.

As to 0.02 precision, with a build like the one inspired you, you will be happy to stain in the 0.5mm ballpark. But having many alu profiles as you say, you could do far more precise build. Something like the cncrouterparts kits. Or round shaft inserted at the slots, could make cheap and precise rail

You can clock the belts on the long axis via shaft at one of the ends. In fact you should. My current machine is build like this.