The noise coming from the Z stepper motor is not necessarily an issue, any time the machine is on and the estop is disengaged there is current sent through the motor to hold it in place.
Did you have the machine up and operational before you wall mounted it or is this the first time assembling it?
I would double check your connections, the plastic connectors can have issues after being unplugged and plugged back in - pins can push out of the back of the connector.