I am not super familiar with the x2 mill however there may be a lock on the z-axis that will keep it at the correct height. Either way if you cnc the machine this problem will be eliminated as the stepper or servo will hold the machine at the correct z height until the stepper is moved. As for the table moving side to side it sounds like your gibs are loose and you will need to adjust them do a search on here or google about gib adustment for the x2.
hope this helps.
chris.
"you don't even need cnc if your handy with a torch"