It is true that Rome does not officially recognize Anglican orders, but this has nothing to do with the papacy. And they do not question the validity of the Eucharist in Orthodox churches. The doctrine of the Eucharist has nothing to do with Peter and the papacy. The doctrine has clear scriptural support and has been the principle worship service of all catholic (little "c" intended) and apostolic churches since the very earliest days.
Very few Jews were Roman citizens and unless one was a Roman citizen, they were personna non-grata in Rome, visitors only.
I can't comment on the accuracy of this statement, but I believe Josephus and other historians mention fairly large and well established populations of Jews in Rome.
Do NC's reject this? Do they believe that the Person that Mary bore is not fully and indivisibly God? Is that why they deny to call her, in complete and reasonable accuracy, the Mother of God?
Boy, you opened a can of worms. You will find the spread of views on the subject, from accpeting the idea while not seeing the necessity of trumpeting it, to outright confusion over who Jesus was.
I have a saying: "Scratch a Maryphobe and you'll uncover a deficient Christology."
SD