gerri,
Thanks for the additional information, as that clears up some confusion. I had the impression that you'd be travelling with the church group and then spending another eight days on your own in Rome and Assisi, prior to the arrival of your friends.
Regarding the day trips to Florence and Siena with the church group, do you know if they've chartered a Bus for those? If travelling by public transit, the group won't have enough time for anything more than a brief look in either city. Perhaps they just want to "tick the box" that they've been there?
It should easily be possible to take a day trip from Gaeta to Pompeii. As you might have discovered, there's no rail station in Gaeta, so this is the route you'll take....
- Bus from your hotel in Gaeta to the Formia-Gaeta rail station (I gather it's not far, so probably not more than a 15 minute trip).
- Train from Formia-Gaeta to Napoli Centrale (about an hour depending on which train you choose). When you arrive at Napoli Centrale, you'll have to go downstairs to the Garibaldi station to connect with the Circumvesuviana. You might find it helpful to watch THIS short video (fast forward to about the 2M:35S mark as that covers the segment you'll be taking).
- Circumvesuviana from Napoli Centrale to Pompeii Scavi (about 35 minutes, frequent departures).
- Retrace the route for the trip back to Formia. I believe the Buses from Formia to Gaeta may stop running about 21:00, so if you're going to be any later than that you may have to use a Taxi.
With the guidebooks, you should be able to find a copy of Europe Through The Back Door at your local Library. I'd recommend packing along a copy of the Italy 2015 book, as I've found that to be a valuable resource when touring cities (the 2015 version should be available this fall - you could buy the 2014 version as there probably won't be many changes). There's a wealth of information there on Museum opening & closing times, how to get reservations, etc.
Which of the five Cinque Terre towns are you planning to stay in? I'd definitely recommend getting reservations early, as they can book up early. What time of year will you be there?