Get the calls right and use all the information you can.
If the kid tries to be honest and says the runner should be safe because he dropped the ball, I say let him receive the benefit of being honest (and that benefit is not always to his advantage - as it wasn't in this case). I would ask my partner if he saw the ball dropped. And then independent of his answer probably rule the runner safe... quietly. I might also ask F2 again "Are you sure? Your team is not going to like it."
The pitch is a different story. If the pitch is so poor that the batter is ducking and can't get out of the way... I don't care if it ticked his shoelace, the award for that poor of a pitch is a free trip to 1st.
As for Fairump/Jerry, I wouldn't have asked to begin with and just yelled dead ball and pointed to 1st. But it hit the bat! Really, you were trying to hit that pitch? I would have disagreed with him but might have allowed him to continue batting if he really wanted too. Although in this case his honesty did prove to his advantage it could just as well have become an out and a disadvantage for his team. The immediate decision to let him continue batting was not immediately to his advantage.
The game situation and the level of competition must be included in your decisions... as they are already. Good umpires always incorporate these influences.
Umpires are not robots we are people and must act personable and understanding. Sooner or later the game is going to be over and you will be off the field discussing the game with the parents and fans. You can just robot your way to the car and leave, but not if you want to raise your level of acceptance as an umpire and work bigger games. Relax from the robotic appearance and enjoy the game... everyone else will enjoy it more too.