Yes, the pitcher is given a strikeout for the at bat
If the runner is in foul territory when the ball hits him, it is a foul ball. If it is a 2 strike bunt attempt, then the pitcher is credited with a strikeout. If the runner is in fair territory the credit would then go to the pitcher, who was the last fielder to touch the ball. My question, then, would be is it an assist or a putout? That answer I do not know.
The batter would be charged with a strikeout and an at-bat, the pitcher would be credited with a strikeout, and a wild pitch or passed ball would also be credited. The batter's OBP would go down as the formula for determining OBP is (Hits plus Walks plus Hit by Pitcher) divided by (At Bats plus Walks plus Hit by Pitcher plus Sacrifice Flies)
Its a live ball
A runner doesn't get a strike, a batter does.
In baseball, in order for a batter to be called out after the third strike, the catcher must catch the ball without it hitting the ground. If he does not, and there is no runner on first base, or there are two outs, the batter becomes a batter-runner. At this point, in order to make the out, the catcher must either tag the runner, or throw the ball to first for a force-out. Regardless of the outcome of the play, the pitcher is still awarded a strike-out. As an illustration, a pitcher can face two batters, and strike them both out. A third batter comes to the plate, receives three strikes against him, but due to an uncaught third strike, reach first. A fourth batter can then come to the plate, strike-out, and thus award the pitcher with his fourth strike-out in the inning.
Anytime a third strike is dropped the runner can advance to first unless he is tagged or the ball is thrown to first before he reaches.
Each time the batter hits the ball, either into fair or foul ground, no matter how much out of the strike zone the pitch may have been, the pitcher is "credited" with having thrown a strike in the "strike-ball" ratio. Since the latter has no effect on the score of the game or in any official statistics, this is not a problem.
It is scored as a strike out for the pitcher (as far as the pitcher's stats) but not an out against the team at bat. The base runner's advance to 1st is scored as a passed ball (error) on the cather.
Yes. In MLB history, that has happened 21 times in the American League and 30 times in the National League. The last time it happened in MLB was June 21, 2008 when Scot Shields of the Angels struckout out the Phillies' Greg Dobbs, Jimmy Rollins, Shane Victorino (reached first base on an uncaught third strike), and Ryan Howard in the 8th inning. Chuck Finley holds the MLB record for most 4 strikeout innings with 3.
The runner is safe, in order for the runner to be considered out the fielder would have to have the ball in his glove or hand and tag the runner. *edit: It depends on where the runner is when he is hit. If the runner is running a direct path to first and is within the 3ft baseline, the runner is safe. If however the runner takes a lane outside the 3ft path, in a deliberate attempt to block the catcher's throwing lane, the runner is out for Interference.
Yes. If the runner reaches first base, it is usually due to an error on the catcher's part, so the scoring is 'K' for strikeout but 'E2' for the catcher dropping the ball. If the catcher recovers in time, then again the 'K' for strikeout is accompanied by '2-3' for the actual putout at first base.