No one knows for sure who first started calling believers followers of the Way. This is probably what the believers called themselves, because the Bible often speaks of a person living his life as if that person were walking on a path or "way," If this is true, the believers were "following the way of the Lord" by living in a way that pleased God.
The "letters" Paul asked for were probably legal papers that permitted him to put Christians in prison. The synagogue leaders in Damascus would have obeyed the letter because it was written by the high priest. If the Romans had seen the letter, they also would have allowed Saul to persecute the Christians, because they permitted the Jews to do as they desired to people who broke their religious laws.
It is clear that Saul saw a light and that it was because of this light that he "fell upon the ground." Some people think that Saul knew that it was the Lord speaking to him without seeing a human form, because the Bible often speaks of God as being light and living in light. Other people think that later in his life he was able to say, "I have seen the Lord Jesus" because it was a human form that he saw here.