According to Uncle Cecil’s Why is a ball always thrown to the 1st baseman as he leaves the field after an inning? the flippee is the first baseman. I presume the flipper is the individual who made the last out.
You presume wrong. The flipper is a person already in the dugout. The ball is flipped to the first baseman even if he is already holding a ball from recording the last out at first base.
It depends. If you’ve got a weak batter who is fast and already behind in the count this would make a lot of sense. It could also be used to distract the catcher from runners on other bases so that they might advance (assuming less than 2 outs already). You see some weird stuff in 11-12 year old ball.
The real problem with this strategy, however, is that in Little League baseball, the batter is out on any third strike, caught or uncaught.
A little history can help in understanding the dropped third strike rule. In its original form the game had no balls and strikes - the pitcher would just keep pitching the ball to the batter until the batter put the ball in play. With these rules, an at-bat could go on for a long time, so they started making changes to the rules to cause an at-bat to end in a reasonable period of time. The first change was to add swinging strikes. From the Knickerbocker Rules (the first written rules for baseball, developed by the Knickerbocker Club in 1845):
In other words, when a batter got three strikes the ball was considered to be in play, just as if he had hit a fair ball. The idea was that, if a batter couldn’t put the ball in play by the time he had three strikes, they would just act as if he had put it in play. If the catcher caught the pitch before it hit the ground, it was like catching a fly ball.
In those days the catcher didn’t squat just behind the batter - he would stand fifteen or twenty feet back (this was before catchers wore mitts, shinguards, chest protectors and masks). The ball would normally bounce before it got to the catcher. The batter got to run on a strikeout pretty often in those days.
Some form of this rule has been part of baseball ever since, even though the game has changed greatly since then. The batter is not automatically out on a third strike - he is out only if the catcher catches the pitch before it hits the ground, or if this doesn’t happen, the defense gets the ball to first base before the batter gets there, or tags the batter with the ball before he reaches first.
And, yes, the reason the batter is out automatically on a third strike if first base is occupied with fewer than two outs is similar to the reason for the infield fly rule: without this exception, the defense could get a cheap double play by the catcher deliberately dropping a third strike.
And, do I remember correctly that if the pitch is in the strike zone, it doesn’t matter if it hits you, it’s still a strike?
Correct. Rule 6.08(b) says: