Yes it is. Law 32 section 3 paragraph e states that a fair catch is made when "a fielder catches the ball after it has touched an umpire, another fielder or the other batsman" (2000 MCC laws of cricket 3rd edition 2008)
If you swing and miss and the ball hits you, it is a strike and a live ball. If you swing and the bat makes contact with the ball and the ball hits you while you're in the batter's box, it is a foul ball and a dead ball.
In regular baseball rules, the ball is still live, even if it hits the ground first, until it hits the batter, then it becomes a "dead ball". If it never hits the batter, its still a live ball.
it is a foul.
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It is a live ball. If the batter reaches first base safely, it is a hit. If the batter is thrown out a first, it's an out.
If it hits the umpire behind home plate, it is a foul ball. If it hits a field umpire who is in bounds, then it is a live ball, meaning that the batter might be thrown out at first, or he might reach first base safely (and then this would be scored as a hit without an error),
Yes.
Should a batted ball hit any base, the ball is considered fair and live and the play continues. It is still up to the defense to field the ball and touch first base before the batter does to record an out.
The ball is dead whenever the umpire calls "time", whenever it goes out of play, when it becomes a foul ball, whenever a pitch hits a batter, or whenever a batted ball hits a runner (and a few other circumstances). It doesn't matter whether the pitcher has it or not. On the other hand, it can't be put back _in play_ until the pitcher has it and is on the rubber.
if the umpire is inside the base path, then it is a dead ball... no pitch --- if the umpire is outside the base paths then it is a live ball
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It is not a dead ball until someone downs (touches) it.