Visiting Tuscany and Umbria

Your time allocations seem good to me.
Rome is not very close to airport. If flight is early then stay at FCO. We use Hilton FCO.
To get to or from Rome airport FCO, book with
www.Rome-Chaffeur.com. They are about the same price as a taxi( which have flat rates.) Or take train Leonardo Express from Termini to FCO.

1. Possibly. Although I would rent a car from the start. Although you won’t need the car to visit Florence or Siena itself, however I’d rather have a car to go to San Gimignano, Monteriggioni, and especially Volterra (which would require two buses with two separate bus companies), than to rely on buses. Consider that bus service is nearly non existent on Sunday. The buses Rome to Siena depart from the bus station located next to the Tiburtina train station. You can go to Tiburtina using the FR train from the Fiumicino Aeroporto station. Bus website below: http://www.sena.it/Home/78-1-en.html.
2. Yes. But consider that 2 nights mean only one full day, so you might scale down the day trips. Distances look short on a map, but roads are often curvy and you can’t drive faster than 25 or 30 mph in most cases.
3. Everywhere you will see ruins. The whole country of Italy is in ruin.
4. If you stay at the airport the last night (and I recommend the Hilton) return the car at the airport. You can walk from the rental car return to the Hilton using the overhead skywalk. That’s what I do.
5. Hilton. Not cheap (200€+ a night) but convenient. If you stay elsewhere you might spend a bit less but then you might need a taxi both going (after you return the car the day before) and the morning of the flight. So in he end the Hilton is not that expensive because it’s walking distance from the rental car return and from the International terminal T3. http://www3.hilton.com/en/hotels/italy/hilton-rome-airport-ROMAPTW/index.html (Book it early and check if websites like Booking or Expedia etc. offer a better deal)

Agree with Roberto, rent the car for the trip to Volterra and San Gimignano. Do Volterra first, and miss the crowds in San Gim.
Just make sure you park outside Siena. The Stadio lot is easy.

If you are in Montefalco or Terni visit the ruins at Carsulae. It is little visited and has Roman ruins that your are free to touch, enter, and walk on. Fun place to touch the ancient history in a personal way. Carsulae is just north of Terni and south of Montefalco, near San Gemini.

Here is Carsulae's website: http://www.carsulae.it/?lang=eng

Thanks everyone!

The reason I was considering dropping the car in Terni was that the thought of driving in Rome intimidates me. We're from a small town and rarely have to deal with city traffic. just how crazy would it be to drive to the airport?