That's a tough question to answer without typing for days. Sometimes the difference can be merely cosmetic things, other times it's in package distribution/management, and other times it can be something major.
First of all, what's the difference between the distros?
A package is something that can be installed on linux. It can be an application like "gaim" or "mplayer", or it could be a library, or even a collection of scripts.
Second, what are "packages"? Is the concept of a package very much similar to the concept of an installer in Windows?
Third, can you have both Gnome and KDE?
It manages windows :) A window manager is what manipulates the windows, and handles the UI stuff.
What does a window manager do anyway?
Not really. Gnome is based on GTK, and KDE is based on QT (If I remember correctly anyways). As long as you have the GTK and QT libraries installed, you should be able to run just about anything.
Is there a distinction between "Gnome programs" and "KDE programs"
Yes. For instance if you have a FS with journaling (like ext3 or ReiserFS), then you wont have to run an integrity check like e2fsck all the time. Other certain filesystems perform better than other under difference circumstances (directory sizes, file sizes, etc). A google search should give you some benchmarks between different filesystems.
Fourth, does the type of file system have any noticeable effect on everyday computing life, to the average desktop user?
Most if not all of the drivers you will need will come with the kernel. For instance, the only driver I had to go out and get was a driver for my video card so I could do 3D. I don't know what will happen to the hotkey functions of your laptop.
Fifth, will I need to find special device drivers somewhere, or should Linux come bundled with the drivers for everything I could possibly have, or does Linux magically not need device drivers? And what will happen to the hotkey functions of my laptop?
Yes. There is a read-only NTFS driver which you could use to access files on your windows partition. You cannot write to an NTFS partition though. One thing you can do to get around this is create another partition, and make it ext2 or fat32. Then both windows and linux could access that partition (you would need to install an ext2 windows driver if you used that instead of fat32).
Sixth, could I access files from my Windows partition from Linux?
Well, most of the software on linux is opensource. This means that you could always modify programs if you so desired. More importantly though, opensource software tends to be more stable and bug-free due to there being more "eyes" on the source code.
what is it that Linux does that Windows doesn't (other than come for free)
Linux also gives you more flexibility than windows. It allows you to choose between window managers, kernel versions, etc. You can also keep file sizes smaller and increase decrease your boot speed by only compiling in the things you need.