All players reacting to fair ball as foul

Question
We had the following happen in our little league game (9-year-olds) and nobody was quite sure how to handle the situation.

With runners on, the batter hit the ball straight down and, without touching the batter or the catcher, stopped and settled on home plate.  All the players assumed the ball was foul (as did the coaches and most of the parents), so none of the runners advanced and the batter did not attempt to take first.  The umpire knew the ball was fair and never called "foul".  Eventually, the catcher picked up the ball, did not tag the runner, and threw it back to the pitcher.  The pitcher proceeded to then throw the next pitch.

Although the umpire knew the hit was fair, he eventually handled it as though it was foul, to which there was no argument because everyone else thought it was foul.  After the inning, he talked to the field umpire for a clarification.  I casually asked how the other umpire would have called it, and he would have called the batter out for abandonment, although I haven't found the specific rule that addresses this example.

So, a few questions:

When is the play over?  
Should the batter have been called out?  
Is there any specific rule to address this situation or does this fall under 9.01 (c)?
What should the umpire have done?  

Answer
Wayne,

According to the rulebook, the umpire did everything he should have, except that he should have called the batter out when the batter quit trying to reach first base.  That is the abandonment rule.  However, I think he did the right thing.  This is a situation where the umpire ruled the right way.  Who wants to call out a nine year old on a technicality when everyone on both teams thought the ball was foul?

Technically, this play is over when the batter stops trying to reach first base.  The umpire should never give direction to either team on what they are supposed to do; they are just supposed to rule on the play.  If the pitcher retrieves the ball and starts throwing home, a the umpire doesn't call balls and strikes, then eventually someone will figure out that the ball isn't foul.  However, they should realize that an umpire doesn't rule a ball fair, they just call it foul.

Hope this helps!

Brian