Questions on Hart Ch. VII and Cohen

1) Consider the following objection: Hart treats judges like umpires. But umpires' decisions are binding; their interpretations of the rules are not (indeed umpires do not issue interpretations of rules). Judges' interpretations of the law are themselves law. That means that the law really is what judges say it is.

2) Is it just vagueness that makes the law indeterminate (as Hart suggests) or do liberal canons of interpretation of legal rules also contribute to indeterminacy?

3) Is the transformation of the law of personal jurisdiction in International Shoe (and in subsequent cases) a product of Cohen-style legal realism? 

4) At pp. 835-36 and pp 839-40, Cohen offers something that looks like a prediction theory of law. Does this theory suffer from the problems that Hart identifies with prediction theories in pp. 136-47 of the Concept of Law?