About train tickets: don't forget to "obliterate" your tickets before getting on the train car.
No one will ask you to see the ticket before riding, and maybe neither while you're.
But, since the tickets can be used within many months from the purchasing date, you must have impressed on them the day and hour of effective departure (it avoids countless using ... ).
So just before you catch the train you must enter the ticket in a yellow square box called "obliteratrice" (you can find many of them on the platforms).
If they find you didn't, you can be hardly fined.