So, it's my understanding that the Cricut cutter can use any of the Cricut cartridges? Doesn't have to be limited to Cricut Cake cartridges?

That is correct. Cricut cartridges fit any Cricut machine. Gives you a lot more options.

Can you use anything else besides the cartridges? Is there a computer program or anything? Just curious if the cartridges are the only option.

there is a new thing that I haven't checked out yet but it the information was sent via email that they have a new "craft room" that you can use to design and do new things with the cricut without a cartridge.. through the computer some how I guess. I don't know but it could help if you look at it.
let me know if you need any other info and I will see what other info that I can find on my email.