The supreme court justice might have some powers to call witnesses if the senate rules adopted to run the trial provide for that but they have not done that here. In any case it is a delegated power from the senators to the chief justice not something inherent in chief justice's power in that role. I think Salmon Chase called or ruled on some witnesses in the Johnson trial because they let him. In the clinton case, rehnquist stayed out of it and was not given that power.
Same thing with the executive privilege thing. They may let Roberts give an advisory opinion on it and then vote on it as senators who make the rules. But that is not the same as saying that he has the power and authority of a judge just because they are letting him function as a facilitator. You know, if Earl Warren sits as the head of the Committee to Investigate the Kennedy Assassination that doesnt make the Committee a court.
