The heater fan should be switched by the ignition switch. Most radios with memory have two 12v(+) feeds, the one that turns on the radio (when it's on) with the ignition is the larger drain, the second wire is full time 12 v and only provides power for memory presets and clock.
If your heater fan is always powered, it could be providing a path for power to leak to other things that also should be controlled by the ignition switch. (wipers, gauges, etc.)
The lack of speeds is probably not a wrong fan motor but the resistor pack. If one or more resistors is burned out, it defaults to high speed. If you only have high speed, it is either bad or 12 v has been wired directly to the fan without routing through the resistor pack. Different speeds on the dash control is supposed to energize different resistors (or combinations) to give various speeds.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI