No. You can't replace a batter, once a pitch has been thrown, unless you want to take an out instead. However, each league has its own rules, but in most leagues, you can't replace the batter.
I guess that would depend on the league and what the league rules are. I know for my cousins little league junior division team you cannot replace the batter once a pitch is thrown.
Yes, the hitter could be replaced; but it will be nice if this is done for a valid reason. Remember you are dealing with children emotions. Treat them very carefully.
No, if the batter has been in the box and chooses to leave the field without hitting or finishing his/her at bat, the batter is out. If the batter is hit by a pitch and can't continue a runner can come in for the batter who would have been given first base anyway.