Front side of the engine, directly underneath the throttle body in front of the plenum.
There is not a separate cooling fan sensor, it controlled by the ECM which get it's reading from the ECT (engine coolant temp sensor)
Yes. A bad or failing temp sensor prevents the ECM from monitoring, and adjusting for, the engine temperature.
Some vehicles have two these days. One is for the ecm and the other is for the gauge. Coolant sensor is for the ecm, I think.
Both "temp gauge sensor" and also the "temp sensor for the ECM" are on the right side top of engine pointing towards the passenger doors front frame in a cross-over tube. The two wire sensor is the ECM sensor and the one wire is the gauge sensor.
That would be the engine coolant temp sensor for the dash gauge only. The sensor near the thermostat housing is the engine temp sensor for the ECM.
The temp sensor for the ECM (engine control module) is next to the thermostat housing.
The engine coolant temp (ECT) sensor monitors the engine temp and sends that info to the engine control module (ECM). The ECM takes in info from many sensors including the ECT to determine the correct air/fuel ratio for the conditions. So to answer your question, yes. The ECT sensor does play a part in fuel control.
It will depend on which engine you have. The 2.0 DOHC has 2 sensors; one for the temp gauge and one for the ECM. The temp sensors are both located on the thermostat housing; one is on top and one is on the bottom of the housing. The Sensor on the bottom of the thermostat housing is for the temp guage. The other i believe may be for the fan but it does not match the sensor for the ECM. Ive been to autozone advanced auto and oreilly, the sensor for the ecm is different than the one on top of the thermostat housing
Damaged wiring or sensor causing confusing information sent to the ECM.
Two wire sensor near the thermostat housing.
If the check engine light has or is illuminated, check for codes, remember this is an OBD I system. I've seen the coolant temp sensor with two wires for the ECM (not the single wire temp sensor for the temp gauge) do that.
Replace the temp sensor. The ECM doesn't know the engine is cold if the temp sensor is bad. You could also check out the throttle position sensor (TPS) and the Idle control servo (ICS).