Does anyone know if I can paint a royal icing crown that has already dried with the gel coloring or should I just stick to the dust?

Not too sure about RI - but I painted gumpaste after it had dried with gel and it got really soft! If you do use gel, use a really light hand and vodka or some spirit since I believe it will dissolve the RI.

Can you airbrush it?

yes - you can airbrush