Balk Move
 

Can the pitcher fake a throw to first base with the base occupied? Actually rotate his arm in a motion to make the runner return. What if he steps off first or steps off, fakes a throw to third and then fakes a throw to first base?

If the pitcher steps off (properly) then he's an infielder and he can fake a throw any occupied base he wants.
I can't visualize the first part of your scenario.

If he fakes to first, without stepping off, it's a balk