You can buy ALL your tickets at the FCO train station if you like. Tickets are sold by segment - no discount (except on specific routes/trains) for roundtrip. For more info on roundtrip "deals," go to
Trenitalia Return Offers.
The airport train into Termini is, by itself, a separate entity. You will have to buy a
Leonardo Express ticket Roma Termini... then you will have to buy a ticket from Roma Termini Station to Firenze S. Novella.
On your return, you will have to have a separate ticket back from Termini to the FCO Airport. So yes, you can buy all your tickets at one time, but tickets are readily available (except during holidays) so you're probably better off just buying when you get to the station - if you like more flexible travel. For help on the trip your planning, here are some other links that make provide some assistance!
FCO Train Station
Riding Trains in Italy
Termini Station – Arriving by Train
Hope that answers your questions! Ciao,
Ron