Can a officer impound a vehicle off private property if he says he saw it on the highway but by the time he arrives at the residence there is no one in the vehicle
"Can he?" Well, did he? If so, then you get to argue it in court. Only the opinion or your attorney, and ultimately the DA or judge, will be of any importance. Yes, police can 'follow a crime' onto private property. You don't get to run and hide, and then jeer them from your property line.
Yes. If he can prove he was in hot pursuit.