I don't think you want to use the Mux4 component. It is for setting an output to one of 4 numeric values. I think you would want to use multiple And2 components. Also you have the the Halui MDI Hal pin names wrong. To call the first Halui MDI command in your INI file's list the Hal pin name should be "halui.mdi-command-00" and the 2nd would be "halui.mdi-command-01"...
To do it you'd need to put the following lines in your hal file. Assuming your button output pin names are "input.0.btn" for the zero button, "input.x.btn" for the X button, "input.y.btn" for the Y button, and "input.z.btn" for the Z button. And since your INI file already has 6 Halui MDI commands listed, adding 3 more to zero each axis would be.
Code:
loadrt and2 counts=3
addf and2.0 servothread
addf and2.1 servothread
addf and2.2 servothread
net zero-btn <= input.0.btn => and2.0.in0 => and2.1.in0 => and2.2.in0
net x-btn <= input.x.btn => and2.0.in1
net y-btn <= input.y.btn => and2.1.in1
net z-btn <= input.z.btn => and2.2.in1
net zero-x <= and2.0.out => halui.mdi-command-06
net zero-y <= and2.1.out => halui.mdi-command-07
net zero-z <= and2.2.out => halui.mdi-command-08
That said, if you are wanting to use a button input that is already used elsewhere in your hal file that is ok. Simply either use that hal signal name to connect the appropriate and2.N.in1 to it, or add the and2.N.in1 to the existing net line.