I use a #2 tip for the outline and a #3 tip to flood in the icing.
When icing the cookies you want to do one color at a time, one section at a time. Let each section dry for 30 minutes or so before moving on.
Pipe an outline of each section and quickly fill that section in with frosting. You can jiggle the cookie softly to get the icing to settle into the outline smoothly without running over. You can do sections that are not going to flow into the first section you've decorated (For the Mario cookies I did all of the white dots first and then filled in the red or green sections once those had dried for 30 minutes).
Cookies need to sit for 24 hours before they can be stacked without disturbing the icing.