Possible explanations of visionary experiences via hallucinaens, etc.

What evidence nis there for Mark having originated in Antioch or Rome? For Matthew being wriiten in Antioch?

Any idea to what extent Paul was reared in Roman or Roman-influenced culture (as opposed, say, to hellenistic / Jewish)?

Acts 4:13 Peter is called "agrammatoi" ("unlettered"). Does that mean "not formally educated in religious matters or the Law of Moses" or just plain “illiterate"?

Hyam Maccoby theorizes that Jesus’ Triumphal Entry into Jerusalem took place, not in the Spring around the time of Passover, but rather in the Autumn during Sukkot, the Jewish Feast of Tabernacles. Further, Maccoby feels that too many events have been compressed into the brief time of Jesus’ entry into Jerusalem and the crucifixion.  It makes much more sense if these numerous events took place stretched out between Autumn and Spring. What do you think?

Can you explain where scholars got the idea that the evangelist Luke was a medical doctor?