I don't think this explanation would really work on a 12 year old. I doubt it will work on most adults, who have been through college, but maybe that's just me.
I haven't gone through all of it, but I've read much of the beginning. It actually starts off with easy proofs of Godel's Theorem, based much more on Computer Science explanations than Mathematical Logic.
By the way, if you're interested in learning actual proofs of Godel's Theorems, you should take a look at this book: http://www.amazon.com/Introduction-G%25f6dels-Cambridge-Intr...
I haven't gone through all of it, but I've read much of the beginning. It actually starts off with easy proofs of Godel's Theorem, based much more on Computer Science explanations than Mathematical Logic.