Can't see textures in geometry window

[micheus]

I am creating new materials by selecting the default material and duplicating it. I suppose there's a better way to do that.

Yeah. In the Face mode select the faces that you want apply the new material and use the context menu (RMB) and in the Material option use RMB for create a new one or LMB for select one already existent. Pay attention to the Information line all the time.