I read that whole thing and just figured out you re a woman. HAhahahahahahahaahaaahahahaha! Wow, it was so apparent I just never saw it until I read that right here. Geesh!
Yea yea anyway, Diahatsu Terios, is a Toyota mini-car. A real lawn tractor. 1.3L 4cyl with 58-90 hp depending on market. It didnt dawn on you this thing was a piece of dung before you got it? Traded in a Civic? What was wrong with that one? Fan clutch? You no has. Electronic fan bolted to the radiator? You has that. Ok, you spun the blades on the PLASTIC FAN? It moved? Good. That tells you its not seized. But you need to know if its coming on.
Generic pictures to demonstrate my point:
a. Cooling Fan Assembly
b. Fan clutch
c. AC compressor-clutch is the black part driven by the belt.
Now that you know what the compressor looks like, and that the fan isnt seized. Start the car up, turn on the AC and see if the clutch on the compressor moves with the belt. If so, count the cycling time between the clutch start/stop. Just watch it, click/clack, click clack and get a time frame for it(seconds on/seconds off). Quick cycling time represents low refrigerant charge. No cycling time means the charge is too low to start the compressor. Long cycling time means adequate charge.
Cooling Fan: has 2 speeds, low, to be used during normal operation and high to be used with the AC. Additionally there is an AC relay which controls fan speed, along with the coolant temperature switch. But you already went through 1 motor so far for some coolant issue and who knows what they replaced when they changed this tiny motor. You cant miss it when its on high because its just like a house fan on high. I dont know where the fuse panel is on this car, but there should be like a 30-40 Amp fuse in the fan circuit. If you can find it and which fuse it is, check to see if its blown.
Fan clutches are only on mechanical fans which are driven by the motor, most often the water pump pulley. Small engines dont tend to have this equipment.
I m thinking your problem is that cooling fan set-up. I dont know if the fan is faulty or just not receiving the signal to turn on. You have to fault trace there, a. is the circuit complete(fuses, wiring harness and power module), b. does it come on, both speeds, c. is power coming to the fan module and not the fan motor or not the module at all? The AC problem sounds like you re not getting enough air past the condenser(the radiator like device, IN FRONT, of the radiator) to effect the heat transfer. Which is why you get cold for a very brief period and then it blows hot.
The compressor send the excited refrigerant under pressure to the condenser to absorb the relatively colder outside air in front of the car from the top to the bottom. The colder refrigerant leaves the condenser at the bottom(condensed but still under pressure) and runs through an dispersion mechanism into the evaporator(which is inside the car mounted in front of the blower motor fan behind the dash). This blower motor blows air past the evaporator where the refrigerant is no longer under pressure but in a gaseous state. The outside air as it travels through the evap becomes cold and leaves the plenum and "conditions the air" in the car/house, or freezer or refrigerator, its all the same principle. Then the gas goes through a dessicant(drying agent) to remove water and then back to the compressor to continue the cycle. Which may also be why you blew the motor the car came with because the fan didnt turn on and the guy you got it from knew this. And the car ran hot in the city(with the AC on) with no airflow coming through the radiator. And you cracked the block and seized the motor.
Find out if the fan works before you do anything. Because if it doesnt you re going to ruin another motor.