What to do with ground wire?
Based on the transducer manual, you should just connect it to case (earth) ground. It's probably just for shielding.



As for the voltage to current signal converter. I don't see any reason it would need an earth connection. Your power supply negative should be tied to earth somewhere anyway.

One last thing, with a component this expensive it's reasonable for you to call up omega and double check this with them. The support is part of what you're paying for.