Some of the comments here make me sad. I'm still looking for documentation on how to remove all the GUI stuff. How do I remove extentions and how do I add them?
when you first boot tc, you have no extensions. i would love if the entire gui was an extension (so long as it was included in the .iso file!) then you'd only need to delete the extension from your "frugal" install (or use a boot code to ignore it on cd) to not load it into ram. gui users would have it just as easy as they do now, non-gui users would have it easier than they do now.
without extensions, tc consists of a bootloader, and bzImage, and tinycore.gz. in other words pretty much everything you see the first time you boot (including the gui) is in tinycore.gz, known as the "core" or the "base."
remastering instructions (on the wiki) tell you how to open up bzImage and tinycore.gz so you can remove things from the base. i realize i haven't answered all your questions, but then i don't know all the answers, so hopefully this is a useful place for you to begin.
(it's also possible to boot: tinycore text to boot into text mode, but that's probably not what you wanted, because all the stuff for the gui is still being loaded into ram and startx will start the gui.)