The fan should not spin when the engine is cold, but it should spin at normal operating temperature.
But the case here is the fan spins when aircond is turned on right? That means the fan is still working. I suggest check the aircond fan wiring and the thermostat. Thermostat should open at normal engine temperature and triggers the fan to turn on as well.
Hard to start during the morning? Probably the spark plug worn out already. Normally that is the case la... if anything is normal.
Kancil overheating problem, Water boiling!!!