There's the bleed screw on the left front of the motor (just loosen it carefully if it has never been or it could snap off).
White smoke isn't really a good indicator if it's cold out, but if it's heavy white smoke then MAYBE the head gasket.

In these short trips, is it still using (loosing) coolant?

Without the the compression and/or leakdown and/or coolant sniffer test, it's hard to tell, especially with the short trips.

There's gotta be a way to test the fan for proper operation, I just know how. I'll see if it's in the Haynes manual.

How old is your radiator cap?