Ang Lee did not win the Best Director Oscar for any of his films. He won the Best Supporting Actor Award at the 66th Academy Awards for his work in The Wedding Banquet.
I'm not sure about all the details of their love story. But they were both well - known in the entertainment industry. They might have met through their work and gradually developed feelings for each other.
Julius Caesar's story is based on actual history. While some details might have been embellished or simplified for storytelling purposes, the main events and his existence are factual.