Absolutely but only if the batter safely reaches first base. A dropped (actually uncaught) third strike is a live ball.
The drop third strike rule only applies when there is no runner on first base. In this case nothing would happen but the batter would be out.
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.
No. You must tag the player or throw him out at first base - or get another runner out by force!!
On a dropped third strike, if there's a runner on first and less than 2 outs than the batter is automatically retired, whether or not the runner from first was stealing on the pitch. If there are 2 out, the batter can try to reach base, and the runner from first would be forced to try to advance to second. As on any other pitch, a runner can always try to advance, but would only be credited with a stolen base if he left the bag when the pitch was thrown, not after it was dropped.
The ball is still on play on a dropped-third strike and a runner can attempt to reach first base as long as a runner doesn't occupy first base prior to the dropped pitch.
The batter is only out on a dropped third strike when there are less than two outs and first base was occupied at the start of the pitch. With two outs the batter may take first base on a dropped third strike even if it was occupied at the start of the pitch.
It is recorded as a strike out and the batter/runner advance to 1st is due to a past ball or wild pitch which ever the case. In this situation the pitcher can record more than 3 strike out in 1 inning. There is no technical name it's just a dropped 3rd strike.
yes, but he can be thrown out if the ball beats him to first after the dropped 3rd strike.
no. force out runner to first base kills the run crossing the plate with 2 outs
All that the rules say is the base must be unoccupied for the runner to advance with a dropped third strike. Now, in your situation there are two outs which changes things a little. It allows the runner on first to vacate the base by attempting to advance to second. If there is a runner on first with less than two outs the batter cannot attempt to take first on a dropped third strike no matter what the runner on first does. In your scenario as well, the bases are loaded so all runners must leave their base in order for the batter to advance to first making it a force play at home plate. All that the defense needs to do is step on home plate with the ball before the runner from third can successfully cross home plate in order to record the strike out.