How much time should we allow, after we land in Rome FCO, to get to the Termini station? Should we make our reservation online before we leave the states, and if we do -and miss our train -(because of unforseen delays) will we be reimbursed or allowed to take the next available train? Also, what if we make reservations and find ourselves able to take an erlier train?
There are so many trains on that route that I wouldn't book ahead of time. Just wait till you get into Rome. Only caveat is to make sure you aren't traveling during the Italian's holiday season which may change things.
It doesnt take too long but there are always things that happen to make it take longer than you thinki it should. I would just grab my tickets at the airport or better yet at the station. (If you are just arriving from a long flight from Seattle... the station is pretty overwhelming.)
To specifically answer your questions. I would allow two hours from the time you land. It will take roughly an hour to deplane, clear immigrations, restroom stop, walk to the train terminal, buy tickets, and maybe wait for the Leonardo Express to Termini. There are 53 trains a day between Florence and Rome so you don't have to worry too much about finding a train. If you a regional train ticket, then it is an open ticket for any train just be ABSOLUTELY SURE to validate in the little yellow box. If for the AVE then it is train specific and if you miss the train you have three hours to get a new ticket or else all is lost.
I would not pre-purchase the ticket for any reason. Just buy the tickets at the ticket office at the airport. It is immediately on your left when you enter the small waiting area for the LExpress. If there is a long line and the train is about to leave you can buy a ticket for the LE at the Tabacco shop directly across the waiting area. But that is all they sell. Then you will have buy your ticket at Termini but the ticket machines are very easy to use == all in English.