Sorry for putting it so harsh.
I did kind of address the deterministic vs non-deterministic aspect of P v NP in the P.S section without explicitly naming the terms I was talking about. I can understand what you're saying and you're right I chose to leave some things out to make it more digestible and because I felt like a rough knowledge of the concepts was enough to understand the larger point.
Anyway, you're very close. If you find a way to weave in that missing aspect you'll nail the subject.
Still thinking about how best to explain determinism vs. non-determinism but perhaps that's best left for another post. Thanks for pointing those things out :)
Yep, that's a tough one. But before you think of how to explain it please consider how you're going to use that knowledge to explain that in a non-deterministic you can solve an NP problem in polynomial time. That's IMO the hard bit.