I believe what you were told is correct
Yes it is part of the plate.
black is not an official part of the plate
Back about 8 yrs ago when I was an ASA umpire, the ruling was that the ball was dead if it hit the plate.
A softball mat is similar to home plate except it is movable, as the plate is drilled into the ground
What is the size of home plate in men's softball?
Yes, it is scored as a home run.
After the softball has crossed over that home plate.