We use a laptop, no lcd at the moment.
We will ground the tubes, put the arduino in a metal box and get some shielded cables for the motors.
We have drawn your logo four times with a pencil connected to the cnc without any problems.
We have run each cut without the plasma cutter turned on and we never had any problems.
When we ran the cuts with the plasma cutter on however sometimes one of the axis stopped working, exept for the Z-axis, this one never failed.
Apparently, only the activated axis fails when the plasma ignites.
As soon as we rebooted the arduino everything worked again.
Before I forget, thanks for sharing your project!