Generally, if your fan does not turn at certain fan settings, the "Blower Motor Resistor" assembly is bad.

If it runs when you don't want it to, I might suggest you check to see if you have the "REST" button pressed, that is designed to run the heat with the engine off, that is what it is for. If "REST" is pressed AND the blower resistor is bad, the fan may run at HIGH speed all the time.

If "REST" is not pressed, I'd say the A/C Heater Control Module is bad, the REST button is bad (shorted) or the blower resister assembly has failed such that it had found a ground internally, allowing the fan to run. (The A/C Heater Control Module usually provides a ground-enable signal, but there is a heavy ground already on the resistor assembly.)

If "REST" is not pressed, I'd order the Blower Resistor Assembly and get it replaced, I'd guess that over 95% of fan control complaints are resolved this way. Everything you need to know is in the thread VALK posted a link to.