The thing is, you're looking too far into this. The deal was (as far as I could tell) that Chzo just wanted his own little perfect lackey to boss around; one who would follow his every request and do things that Chzo was unable to do.
That was it exactly. He lied to EVERYONE because his only goal was to make the New Prince.
He was. The deal with Cabadath was that he never actually died, and as such he kept some of his... humanness. For example, throughout all the games, he's trying to make sure he doesn't get replaced. If he were a perfect lackey, he would do whatever Chzo wanted regardless, instead of going behind his lord's back to save his own ass. The New Prince was, more or less, something that Chzo created with none of his humanity left. Theo DeCabe (and John Defoe) were both completely dead before the New Prince was created. Does that make sense?
tl;dr, Chzo wanted a perfect lackey and screwed everyone over to get him.