There really is no limit as to what you can combine together. Take a look at F1, Indy, or even the WTAC cars. They run wings, upon splitters, tunnels and diffusers. You are correct in that a wing creates its own downforce. However, the downforce is not really spread through the whole car. Overall downforce is split into front and rear sections. For example, adding a rear wing to a completely neutral car will result in a rear bias. Running a splitter only will result in a front bias. That is why I say aero is all about balance; you have to play with the size of each device to get your car to handle the way you want.
A spoiler, on the other hand, works by disrupting the airflow. Laminar (more or less) airflow hits the spoiler and is, for lack of a better word, spoiled. This creates drag, and more importantly, a high pressure region. Behind, or on the other side of the device, a lower pressure region is created. Spoilers are usually added to the back of the car, so it creates a low pressure region behind and slightly underneath the rear bumper. Low pressure tends to suck other air towards it (much like other things, air flows from high to low). Canards do act the same way, though it really depends on the shape of the canard. Flat canards do not do this; rather they create a vortex simply due to shape. A rear diffuser is shaped exactly like the bottom of a rear wing. I'll touch on that later.
The car in the first pic is a customer car. My rear wing mounts are designed so they are the furthest back they can be, allowing the endplates to be used as mounts themselves, thus freeing the underside of the wing to create as much downforce as possible. The reason the spoiler is there is help induce the lower pressure pocket that exists behind the car from any air that hits it. I'll admit it doesn't do much, but that was a choice the customer wanted to make. Another benefit from having the wing that far back is you can create a longer diffuser. A well designed wing will help drive the air flowing through the diffuser, again due to the low pressure created underneath it. The endplates are as large as they can be to maximize downforce and keep the high pressure and low pressure regions of the wing away from each other as much as possible. Since the control arms are still left in an open pocket, there is not much point in creating another diffuser area behind here.
-Henry