Why does my object not have a material? I can't assign smooth shading to my object (clicking smooth in the shading tab on the left side yields not result). When trying to find out why I noticed that it doesn't have a material in the material panel (bottom right). Why?

This is a custom shaped object I made from a cylinder mesh.
On the bottom right, scroll up and you will see the panel to add materials.
Even if you don't assign a material to your mesh the smooth shading option should still work.
From what I can see, your mesh just has inverted normals. 
Go to the panel on the left and click "Recalculate"
if that doesnt work, then click "Flip Direction".