I have a connection in Italy coming from outside Schengen area flying to outside Schengen area, and I'm wondering if I need to go through immigration and customs in Italy or not. The flights are separate reservations but it's the same airline (Alitalia) and same airport (FCO) and the waiting time between the flights is about 3.5 hours.
There's no difficulty at the airport itself; it is an international airport well equipped to handle transit passengers. Unless you need to re-check a bag, you will not need to go through immigration or customs. Simply follow the connecting passengers route. If you have been unable to check in for your onward flight, you can do so at the transfers desk without going landside.
Your problems come if you are taking luggage—unless you can convince your check in agent to through-check onto the next reservation, you'll have to retrieve your bag and check it in again. You have adequate time for this unless your first flight is significantly delayed. Of course you would need the appropriate permission to enter Italy to do this.