There is no true answer to this. It depends on the particular field.
about 90 ft
Safeco field in Seattle, WA
For Little League (7 - 12 year olds), the distance is 60 feet.
46 feet. http://www.sportsknowhow.com/Baseball/field-dimensions/little-league-baseball-field-dimensions.html
In Major League Baseball, the bases are 90' apart. The distance from home plate to the nearest fence is 250' or more.
It depends on the specific baseball field you are referring to. The distance from home plate to the center field fence can vary between 400 to 440 feet in most Major League Baseball (MLB) stadiums.
How far is it from 2nd base to center field? The distance from home plate to 2nd base is 127.28 feet (use pythagorean theorem z^2 = x^2 + y^2 or z = sqrt(x^2 + y^2)), so the distance from 2nd base to the fence in dead center is 277.72 feet.
Official fields use 90ft baselines and 60ft6in from the pitchers mound to home plate. The fence distance is determined by the team.
The right field is located on the far right side of a baseball field when facing home plate.
Yes.
Rubber
The distance from the pitching rubber to the back tip of home plate in professional, college and high school baseball is 60 ft. 6 in. In some leagues 13-14 will pitch from that same distance, but in some they will throw from 54 ft. as a transition from little league to high school. I would check with your rules for your league and work from there.