"So, I gather that the following are all legal moves:
B d1-4,
B 4-d1,
B e8-5,
B 5-e8"
That is absolutely correct.
"So, it looks like the diagonal from 4 to the first rank is a different color than 4, and the diagonal that goes from 5 to the last rank is a different color than 5, and that is how the color changing is done."
By the way: The squares 4 and 5 do not have a uniform color. The squares are each composed of both colors. This is the only way to make a color change possible.
"So, I gather that the following are all legal moves:
B d1-4, B 4-d1, B e8-5, B 5-e8"
That is absolutely correct.
"So, it looks like the diagonal from 4 to the first rank is a different color than 4, and the diagonal that goes from 5 to the last rank is a different color than 5, and that is how the color changing is done."
By the way: The squares 4 and 5 do not have a uniform color. The squares are each composed of both colors. This is the only way to make a color change possible.