backing up system image before rooting: please help
First, there is no such thing as a "full copy" of the system stored anywhere on the device, as it is with the Windows recovery partition you describe. Neither is there a "program which reinstalls the android operating system from scratch" stored on the device, so you could back that up (installation is always done via rom-flashing, which takes care of itself).

Second thing is a chicken-and-egg problem: in order to create a partition-image backup, you will need root access -- so you cannot do that backup before your device is rooted (and a custom recovery is in place to provide the necessary tools). But then you no longer can backup the original state, as that has been altered by the rooting process (and custom recovery installation). So the only way to have the "real stock state" available is to download a stock image.

However, the rooting process itself is reversible (see the unrooting tag). And with a full stock installation archive (including the recovery and everything), you should be able to restore the "pre-rooting" state. Not having a Samsung device, I can however not tell about any flash-counters which would let Sammy know what "dirty work" you did in between...