It is referred to as the "backstop"
There is no batting cage behind home plate.
No. The Home Plate Umpire, the Catcher, and the Batters are in foul territory, because they are all positioned behind the foul lines.
Behind Home Plate.
408 feet
325 feet
Usually in the cage behind home plate where the radar gun is located.
The distances are measured from the tip of home plate to the bottom of the fence.
Depends on the field in question. There is no standard.
draw a line from home plate accross second base to the fence. divide the line from second base to the fence in half.
The Home Plate Umpire...
Safeco field in Seattle, WA
In Major League Baseball, the bases are 90' apart. The distance from home plate to the nearest fence is 250' or more.