Unless you've got a 1st class pass you can't take the direct train between Roma Termini and Fiumicino Airport (the so-called Leonardo Express). On the other hand you can take regional trains from Roma Tiburtina. 

If it is your only journey of the day do not use a pass day, tickets cost less than 10€.

Use your 4th pass day for a day trip from Florence to Pisa or somewhere else.

In Italy there are :

- Freciarossa & Frecciablanco high-speed trains 10€ mandatory seat reservation

- Intercity trains 3€

- many reservation-free (slower) RE and regional trains

If you miss your reserved Frecciarossa/Intercity train, then either take a regional train or buy a new seat reservation. It shouldn't be a problem even of the day of the travel.

If you miss your train due to a previously delayed train then speak to staff and you'll be able to take the next train free of charge

You can check reservation-free itineraries on bahn.de or many other planners.

Book the seat reservations for Italy on tickets.oebb.at (no booking fee) -> add Eurail as a discount and select one-way tickets

Let us know for questions

Actually, I got a spare 4th pass day because the other days I rent a car to travel. I purchased 1st class pass indeed, so do you mean I can travel to the airport without a reservation?

You simply need to add the Leonardo to your trip and pass as normal. It is an open seating train so no reservation necessary.