Since 1901, 94 players have homered before their "age 20 year" - which is their age on June 30. This may exclude a few players whose birthdays come before June 30 and homered before their birthday on that year, and vice versa, but the number should be about right.
Tony Conigliaro of the Red Sox with 24, all coming in 1964 at the age of 19.
All of them.
zero
27
darryl strawberry and rusty staub
No. Through the 2010 All Star Game, there have been 175 home runs hit by 133 different players but none by a pitcher.
25 players
Miguel Cabrera
65
104
2 players hit 40 or more home runs in 2008, both from the National League. R. Howard(47), and A. Dunn (40)
As of the 2008 season, 97 players have hit a home run in their first MLB at bat. Click on the 'Players with a Home Run in Their First At Bat' link below to see a list of those players.