"How is it scored if the player reaches first after a dropped third strike? Is it E2?"
Usually not, but it depends on exactly what happened.
Example 1: the batter swings and misses at a pitch for strike three, but the catcher is unable to hold on to the pitch, allowing it to hit the ground and the ball then rolls away from the catcher. The batter is able to make it to first base safely before the catcher can retrieve the ball and throw it to first. In this case, what you have is a passed ball, NOT an error. It is scored as a strikeout, with the batter reaching first on the PB.
Here are the OBR references:
OBR 10.14 No error shall be charged in the following cases: (f) Because the pitcher and catcher handle the ball much more than other fielders, certain misplays on pitched balls are defined in Rule 10.15 as wild pitches and passed balls. No error shall be charged when a wild pitch or passed ball is scored...(1)(ii) When the third strike is a passed ball, permitting the batter to reach first base, score a strikeout and a passed ball.
10.15 (b) A catcher shall be charged with a passed ball when he fails to hold or to control a legally pitched ball which should have been held or controlled with ordinary effort, thereby permitting a runner or runners to advance.
Example 3: just like in the first example, the batter swings and misses at a pitch that the catcher is unable to hold on to, allowing it to hit the ground. However, this time the catcher pounces on the ball quickly, and throws to first in time to retire the batter. But the catcher's throw is high, and sails past the first baseman into right field, allowing the batter to touch first base safely. In this case, we DO have an E2, not a passed ball. The batter did not reach first base because of a passed ball, but rather because of an errant throw.
Example 3: the same thing happens as in Example 2, but this time the catcher's throw to first base is a good one. But now the first baseman drops the ball, allowing the batter to touch first base safely. This is scored as a strikeout, with the batter reaching first base via an E3 (the catcher would also receive an assist on the play, but that is another topic!).
(I have edited this post slightly to clarify that the uncaught pitch was a third strike, and to add that the catcher would receive an assist in Example 3)