At work, super busy, but some quick responses and I will be more detailed later.
Your cabinet is really close to mine. Yours is definitely a later model machine as the yellow Hurco tag is the dead give away for that.
The spindle motor can be re-wired very easily to use the LV 220 side. There should be 9 leads (I think 9, may be

that are in the motor. You change up the leads and that will make it either the 220 or 440. 440/480 was the norm for just about all factories. Not many step above 480 to the machinery. Once again, 440/480 would cut the electric bill in half compared to using 220V.
Looks like VFD was ripped out for some reason.
Yes the single phase out of the transformer will supply all 3 of the amps at one time. This is where you can follow the wiring back to the left side cabinet and get power to the transformer.
Not sure of the air piece on the side... definitely looks like a air solenoid and my guess is that is a "cool mist/air system" that would have had a line going over to the spindle area for blowing refrigerated air onto the parts during machining. It looks to be in the same place that most of the coolant lines bolted, so that is best guess.
No need to take anything apart at the limit switches (Proximity Switches). All of the wiring comes back to the TB-8 connector and then over to the limit switch board and then over to the amps and back down to the computer card cage. I will take pics and show you where to tie in as there is no need to take anything apart anywhere else on the machine for the proximity switches. I took all of it apart to trace it, only to have to put it all back together with nothing done to any of it. You did find them as they are identical to mine.
Most all of the work you will do is in the one right hand cabinet. If you do what I did, you should be able to get the machine fired up pretty quick. Very little work to do everywhere else as most all the wiring from all equipment terminates in the right hand cabinet.
Hope this helps until I can respond tonight.
Robert