Okay, no problem. I don't normally say micro-code but I chose to since you already had. The network card doesn't have what most would think of as a processor, since most think of the CPU when they think of a processor. If you think of the CPU as the brain of the computer system then yes, the network card does have a brain as well (in the form of a chipset).

Firmware is just software that is written onto read-only memory (ROM) chips. Those chips make up the chipset. Drivers are software that communicates directly with the hardware. If you don't have drivers installed (or you have incorrect drivers) then your software that use (Windows, iTunes, Firefox) has no way of talking to the hardware. The hardware can't do anything on its own.
The way you describe it is correct all the way to the point at which you get confused. The driver gets replaced because whenever you update a driver Windows will keep a copy of the old one so if the new one doesn't work (for any reason) there is something to fallback on. Since the hardware is critical to the operation of the computer, Window's keep an extra copy. That is what the "Roll Back Driver" option is for under the device properties in device manager.

When Windows does a System Restore checkpoint it is only backing up the files it needs to run. It backs up the current and previous drivers, the registry, all the OS files, Windows settings, and program files. Pretty much everything except what you would find in your user profile. That is why you have to use a back up program to back up all your personal documents.
If you want a really in-depth and clear explanation of how to update your device drivers then you should
read this post by Scott Mueller (the PC hardware guru).

Evan
P.S. Sorry for the delayed response.