Can a pitcher fake a throw to 1st base when not in contact with the pitching rubber?
The only time a pitcher is allowed to fake a throw to 1st, is after they step backwards (towards second base) with the foot that is engaged with the rubber. That foot has to be the first thing to move, once the foot is disengaged backwards, the pitcher can do what ever he wants. For a right handed pitcher it would be his right foot. You can fake a throw to 2nd and 3rd, as long as your movement is clearly in the direction of that base. You can lift your leg to throw home and step to third or second and fake a throw to that base. Make sure that the lead foot (left foot for a righty), lands inside the 45 degree angle when going to third and the land foot lands clearly past the rubber on the backside when going to second. At second base you can also do a spin move and fake a throw.
