welcome to the italiapass community. To hopefully help in answering your questions, first the tickets from FCO (Fumancio) to Rome Termini do not have a time restriction and can be used any time during the travel day they are booked for. You can always book tickets to Florence at Rome Termini when you arrive there so you are not worrying about missing your train. If you do purchase in advance and select a flexible option that allows for changes they can only be changed up to two hours prior to departure, within the two hours they are unchangeable and if you are booked for a high speed train if the train is missed you would need to purchase new tickets. Regional trains do have a 4 hour window of availability to take a later train if the initial departure is missed. Children under 4 are free as long as they are in the lap of an adult for the travel and only require a ticket if they need their own seat. If that is the case child tickets can be purchased online with your order or at the station.