My setup goes something like this:
*I prefer Wilton as it has a more paste-like consistency rather than gel and I think it dries better.
*I prefer to put my colors out on a palette and let them dry so I can use them just like watercolors, but I will use fresh.
*I don't dilute the colors in the palette. I dampen my brush and take on the color as needed. Darker, more opaque colors needed? I take less water onto my brush, sheer, lighter colors: more water.
*I HATE HATE HATE white food coloring! For me they never dry, it muddies up everything and I do not use it. Did I mention that I hate it? One of the very rare exceptions for painting with white is the blackboard cookies. On those I use CK powdered white food coloring which works amazing and actually dries. I also use water with that.
*The black can be a "problem" color and I will put that in my palette and pour alcohol over that so it dries it out better. If there is ever any smudging, it's from the black so I find this helps. I also will use powdered black if I'm worried.
I hope these tips make sense! There are several ways to paint, and this is just the way I do it. I know a lot of people use white, but for some reason, it doesn't work well for me. If there is white in my design it is because I've either worked around the background white of the frosting or do a wet on wet white.
The mermaid cookies: Those are all wet on wet, except the outlines were painted in a dark brown.
One other thought: cookies can take a lot more water abuse than you would think I have painted, "erased" by brushing off all the color with a damp brush, repainted, and even repeated that process again before on a single cookie. I think the key is that your royal icing has some corn syrup in it. It helps to make a nice canvas that is more "waterproof".