You are correct, if you measure the rotation in a horizontal plane, you have to apply the same correction factor as for the Foucault pendulum: multiply by the sine of the latitude. So it would turn 15 degrees per hour at the poles, but only half that at 30 degrees latitude and would not rotate at the equator. The guy on the youtube video I posted had the correct idea: place the gyro on a plane that remains parallel to the equator and align the gyro axis perpendicular to the direction to the North Star. Unfortunately, I believe he doesn't align it correctly (although, because he is close to 45 degree latitude, this error is not too big).
No, I don't think a DC motor would align with the Earth magnetic field. But I'm not too sure why the heading indicator and several other instruments on airplanes typically work with "vacuum".
Edit: A small, cheap, DC motor with just two poles would align with the Earth magnetic field. Motors with a large number of magnets should not do that.