No. The cable modem itself has a MAC address, and that's all that the cable provider can see...
2) If I take my computer at home and plug the modem into another outlet from my provider the MAC will remain constant, but my IP will change...
MAC address is always constant. Period. The IP will probably not change. For you to understand this you have to realize that although DHCP assigns IP addresses dynamically, it generally gives you the same address if the addresses has not been reassigned and you still are within the lease period. This can be explained in a far more complex matter, but that's the general overview/idea.
3) At work (on a huge network), I have an IP address for my machine. Assuming I leave it plugged into the same port (and the IT folks don't do magic on their end), I should have the same IP address daya fter day after day, no matter how many times I reboot.
Not necessarily. I'm about 99.9999% sure, but the addresses will be reassigned if your lease period is over. Then again I'm not sure if it will reassign it if you are *actively* using a connection (sending frames and receiving them) and the lease expires.
4) an IP address is not "coded" to any part of hardware (like a MAC), it's something the OS picks up and indicates to you when you ask for it...
That is correct. IP addresses are *not* coded. You can have an IP address when you're at home using your cable, and if you pick the computer up and move it to your neighbors house, you'll get another one (assuming he is using DHCP, etc.)
Am I starting to understand correctly?
Sounds fairly accurate to me