More Baseball Rules Discussion

I got into a discussion with Sean yesterday about the post I made a couple of weeks ago concerning when a runner has officially taken possession of a base.  We consulted the rule book (online at baseball-almanac.com, a great site) and found no specific details about the situation.  (Though, admittedly, I did not carefully pore over every bit of it research-style, since we were simply having an entertaining discussion.)  While shifting through various alternative scenarios to try to tease out the answer, this fun one came up:

What happens when a pitch never reaches home plate?  What if it stops halfway there?  Presumably, we decided, it must be called a ball, but how far does it have to travel?  If a pitcher drops the ball while set, that's a balk.  So where is the demarcation between balk and ball?

Interesting things hinge on this: When a squeeze is on, the pitcher could "throw" a ball at his feet, then pick it up and fire home, which would prevent the batter from being able to bunt the thrown ball (on pains of being called for interference). When you want to intentionally walk someone, why not just "pitch" the ball directly to your feet, thereby avoiding the risk of throwing it past the catcher or accidentally for a strike?

One other note on the scenario posted earlier: If it is when the pitcher toes the rubber that "freezes" the situation (i.e., a runner at first base at the point the pitcher toes the rubber will need to tag up at first base, no matter how far he gets before the ball is pitched), then strange things can happen.  Say the runner is on third, and he takes off and scores while the pitcher is still in the set position.  Then the pitcher will have no incentive to EVER pitch the ball, since doing so will concede the run. And what happens if the batter calls time?  Can the catcher call time after a runner has scored but before the pitch is thrown? These situations are all derivative of the scenario I outlined a couple of weeks back.  They suggest that it can't be the pitcher's taking to the rubber that starts the play.  Clearly, if the runner scores while the pitcher is still standing set on the mound, the run must count immediately, right?