Is it possible to take a train from DaVinci Airport to Castiglioncello?
Without checking schedules, probably not as you would need to go into Rome first. Assume you can get from Rome to Castig... Have you checked the trenitalia.com schedules. Or use bahn.de for just routing/scheduling info.
Yes. It will require 2 train changes. The first one in one of Rome stations (which stations will depend on which time and train), the second one at another station along the Tuscan Coast (Livorno, or Campiglia, or Cecina). Which one will also depend on which time and train you take. You can get all the schedules on trenitalia.com enter FROM: Fiumicino Aeroporto TO: Castiglioncello Date: use a date within a week from today
Hour: enter 00 to see all possible solutions starting from the first one in the morning. Search.