it is always the first pitch
Over at Baseball-Reference.com each hitters record shows his batting average for each pitch in the count on the Splits page
William Howard Taft was the first to open the major league baseball season by throwing out the first pitch on April 14, 1910. McKinley threw out the first pitch in a minor league game as governor of Ohio before he was President.
Hitting the first pitch? Yes that's probably a record. The record for the most home runs in a row is 4, but they weren't all first-pitch swings.
100.9 mph by Nolan Ryan
That is a record that will never be known. Pitch counts in baseball have only been important in the last 25-30 years. Before the mid 70s or so pitch counts were not a statistic that teams kept.
The first pitch.
Fast pitch and baseball are the same. A softball glove is different.
Softball pitches have been measured at faster than the record baseball pitch of 104 mph.
First Pitch Strike percentage - or the percent of times their first pitch to a batter results in a strike.