The gurgling sound is water filling into the heater core, you probably have a small leak somewhere and thats what causing the expansion tank to not work either. It can also be a wrong or bad radiator cap, the leak is causing a vacuum loss in system, thats why its not sucking liquid back from expansion tank.
The diesel edition corolla used a mini cap radiator with twin cooling fans which run on the old series/parallel type 2 spd system, its switch to kick the fans to high is in the thermostat housing on the engine, while the low speed it the ac unit
The petrol one uses a microcap radiator and single cooling fan that runs off two relays and a resistor behind the headlight to work it as 2 speed. Its ecu controlled.
To make the fan work as original you need to wire it like the petrol one with two relays outside and a resistor (forgot impedance and wattage)
Or you can place a spal, bosch, mishimoto fan ecu to control the fan via pwm in 6 speeds.