Wow, that is a lot of questions. I'll do my best but maybe the others that have done this more than one time can chime in as well-
The train line we took (The Circumvesuviana line) didn't run all the way to Pompeii early in the morning. The ticket office told us we could ride to Ercolano (The Herculaneum stop) and then be able to get down to Pompeii from there. So we ended up buying two tickets one to Ercolano and one to Pompeii. You can certainly ask if you can buy the ticket "all at once", but its a commuter line so it may not make much if any difference in cost. We ended up buying a ticket from Pompeii to Sorrento also and then one in Sorrento to take us all the way back. We probably could have saved money and bought the full two way fare ticket, but we did not know if we would ahve time to do all of it, so we eneded up buying it in pieces.
Note there there are no reserved seats on the commuter lines so you don't have to worry about times. You can just get on the next available train when you are done seeing Pompeii or the Herculaneum.
I don't know why you couldn't see trains early in Livorno to Pisa. We got off the ship as early as possible and took a cab to the station and we got right on a train. This was as soon as you possibly could have gotten there from the ship. It was again a commuter line. The trip is only about 10 mins to Pisa, its not worth getting an 1st class ticket even if you could. I wouldn't worry about getting your tickets now for Pisa. Go to the station and talk with the ticket office, every one of them had someone that spoke enough english to help.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013