OK - the fuzz on the screen when the spindle is running is happening because the monitor has been replaced with a new style one. Haas do a replacement cable that will stop this from happening but I am pretty certain that other than fuzz on the screen it will not cause axes problems. It is definately worth getting the cable though - I will try to get you a Haas part number for this.
Can you explain to me a bit better what is happening with your x and z axes? Is the Z axis dropping? What alarms do you get? Do you get x axis z channel alarms and do you get z axis z channel alarms? how often do you get these alarms? will the x or z axes move or run at all? does the y axis work ok?
The ground fault detect alarm is probably just beacause the software is different to what you had before. What software did you have before? The ground fault alarm can just be turned off - since we already know there is not a ground fault.
The 'no interrupt' alarm is a tricky one. Sounds like a problem with low volt power. How often do you get no interrupt alarm or does it not reset? To possibly fix 'no interupt' - try this:
Locate the power distribution PCB
It is top right side of electrical cabinet
It has around 3 circuit breakers on it including 'coolant' 'main transformer'
Once you have located this PCB (and with machine powered off)
Unplug each plug and then plug it back in - do this three or four times on each plug. Only do this with plugs on the left side of the PCB. You can do it with all plugs if you like - but the issue is probably with one of the plugs on the left side. The reason for doing this is the pins in the plug are not contacting properly due to oxidation or just weak spring in the plug.
Hope this helps