The First Questions about Luke

1. How do we know that Luke travelled to different places to get his information?
We don't know all the places he went, but since he claims to have had eyewitness information, he had to at least travel to the lands of those who saw or participated in the events of the life of Jesus. We also know that he was a travel companion of Paul, which shows that he was a veteran traveller.

2. What kind of physician was Luke?
It is in the context as a travel companion of Paul (Colossians 4v14) that we find out that Luke is a doctor. Also, in a letter to the Corinthians, Paul reveals to have some physical ailments and injuries, we conclude that Luke was likely his physician doctor. Luke was not a magician doctor. The disciples never used or endorsed the use of magic to promote or further the work of the gospel (see the story of Elymas the Magician, Acts 13v4-12). Luke was also not into the use of superstition in order to diagnose or cure sicknesses, since Paul makes a big point in a letter to Timothy to avoid all such nonsense.