Tickets to climb Duomo Florence & regional train tickets in advance

I can only answer 2)

You can buy regional train tickets anytime until just before departure. The trains do not "sell-out". If all the seats are taken, you stand until someone gets off and you can get their seat. In practice, if you are boarding at the train's point of origin, just show up 15 minutes early and get on when they spot the train on the platform and you'll be the first get on and have your choice of seats. That would be the case for Rome-Terontola and Florence-Pisa. For Terontola-Florence, that will be a continuing train, so you just find whatever seats are available.

1. https://duomo.firenze.it/en/home
2. In short, just like city buses the Regionale trains can't sell out. Tickets are not train-specific, but route specific. Hence the need to time-stamp the locally purchased tickets before boarding and to get on within 4 hours. Regionale tickets purchased online on the official sites are pre-stamped and do not need to be printed out.

Thank you! I do have the trenitalia app downloaded so I think we will buy tickets on that once we know for sure our timing. Since the online tickets are pre-stamped, does that mean you are obligated to get on the specific train that you chose (aligned to a specific departure time)? I would assume so..... thanks again!

No, it means that you are obligated to take either the picked train or another regionale making the same route and departing within the following 4 hours.

Since the app lets you buy any train ticket up to 15 minutes before the scheduled departure time, the 4 hours rule has become quite pointless for those who get tickets on the Internet.

Had no trouble getting tickets same day to climb Duomo a couple weeks ago.

Regional trains don't change in price, no need to buy in advance.