The manufacture is incorrect, China they don't have to have a Ground, every other country in the World you have to use a Ground, very unsafe with out it, that is why you buy the right spindle to start with and it will have a Ground
It's not ideal to run an individual Ground wire, but should work until you do it correctly, with a 4 wire shielded cable the cable you need is from IGUS CF6-15-04
There seems you have a problem with your U V W wiring, most likely at the Spindle Plug
There is more than one thing that can cause a E O C A fault
# 1 is usually wiring you have a short
# 2 the Spindle has a short in the windings
# 3 the VFD has a faulty current sensor
# 4 the Parameters have been set incorrect for the Spindle you are using