Before you can really get started with texturing your objects, they need to be sent to Element 3D. Let's start with the lamp (as that's the most complex object that we've made so far). The lamp has several objects that we want to be able to move independently. For example, if the table gets bumped, we'd like the shades to rock a little to add some more realism to your motion.
Element 3D simply won't recognize that your shapes are objects that are separate from your lamp (because of the export/import process). The way Element 3D breaks objects up from one file into several items is done through surfaces (textures, shaders, or materials).
First, make sure that all of your lampshades are centered over your light sockets. The exact procedure covered here differs slightly from 3D package to 3D package, but the principles are the same. For each object and each different surface, assign a unique shader.
The colors that you use in your modeling software are irrelevant...