So they airbrush the picture on the cake????

So how do they do that?
Cake decorating is getting pretty high tech it seems to me.
So how do they transfer a picture onto a cake? Is the color just food coloring? The kind I used to color easter eggs with when I was a kid?
How do they get the black color?

You pretty much answered your own question.

Yep “they” air brush it. Food color is they dye in question. There is black food dye (ever heard of licorice?)

To get the picture to the cake, a kind of projector is used. Very similar to the overhead projectors in schools. Yes you do pay for copyright fees for comercial designs. Ever wonder WTF at a Claire Bare cake?

/ mom was a decorator in a commercial bakery

They print photos on cakes now, with an inkjet printer, loaded with edible inks; the picture is printed onto a special sheet of edible stuff that is halfway between rice paper and sugar icing, then this is stuck to (and becomes part of) the top of the cake using conventional fondant.

      • Yes–I work at a store that makes these photo-cake decorations. They have what appears to be a computer printer (but it is a stand-alone device, it isn’t hooked up to anything else except that it is plugged in to the wall electricity) and it prints (or copies? I never asked really) with edible ink, onto special paper. Then the paper is laid on top of the cake with fresh/wet icing, and the paper just dissolves, leaving only the ink.
        ~

PhotoFrost Icing Sheets