(i) Yes, the prospect of meeting Stephen Hawking made the writer nervous. He was to meet a great personality and that too one who had achieved greatness despite his disabilities. Clearly, it was a big moment, a great honour for the writer. So it is not surprising that he was nervous at the prospect of meeting Stephen Hawking.
(ii) Yes, he felt excited at the same time because it made him stronger to see somebody like him achieving something huge. This made him aware of the many possibilities present before him, thereby helping him to reach out further than he ever thought he could.