The door is already painted in white…Will have a cupcake painting/mural on top…can I paint on top of the old paint? Or have to remove the old paint? Do I request a door with no paint at all?
If the door is in good shape then there is no need to strip off the old paint. Simply clean and prime the door to accept the new paint. In many cases even priming isn't need, if the existing paint on your door is acrylic and well adhered.
To tell what type of paint you have you will need to use some denatured alcohol and a clean rag. Check out this article for info- <a href="http://www.house-painting-info.com/kind-of-paint.html">What Kind of Paint Do I Have?</a> When in doubt prime the door.