W.P.S.,
1. Yes, to fake a throw to 1st base, the pitcher must step back off the rubber with his pivot foot prior to breaking his hands apart. He is allowed to step in the direction of an occupied 2nd or 3rd base and fake a throw there from the rubber.
2. The pitcher, while in contact with the rubber, can only do 3 things legally:
a) deliver the ball to the batter
b) step and throw to a base (or feint toward 2nd or 3rd)
c) disengage the rubber by stepping backward with the pivot foot
So, to answer the question, no, the pitcher cannot do as you described. He cannot in any way fake a throw from the rubber to 1st base. If he turns toward 1st and does not throw, it is a balk. It is also a balk if he hesitates and then throws. It is also a balk if he throws to F3 who is playing off the base with no chance of making a play on the baserunner. F3 must be considered close enough to tag the runner or it is a balk.
Once the pitcher legally disengages the rubber by stepping backward with his pivot foot, he can fake or do whatever. He essentially becomes an infielder at this point.
3. You are correct. His very first movement from the windup position must be a step backwards with the pivot foot. If he starts any other part of his motion and then tries to step off, it is a balk.
Another key to remember is that from the set position, the pitcher does not have to come to a stop when throwing or faking a throw to a base. He must come to a complete stop prior to delivering a pitch.
I hope this is of some help. Maybe others can chime in with some helpful hints. Find your rulebooks!
Steve