IF the car is AWD, as opposed to 4WD, it should have all four tires replaced at the same time, AND they really SHOULD be sequential serial numbers, too IF possible. This is because of the viscous coupling used in AWD vehicles. Any difference beyond a certain point in tire height can burn up the viscous coupling. The tires must be very close if not the exact same diameter, so that much was true.
This is not true however for the 4WD Escapes with the switch on the dash that controls a sho nuff transfer case, like the 04 model we have.
I don't know anything about the cooling system debacle, as ours has the 3.0L V6.