6 You can get to Herculaneum on your own by train. 15mins walk to Train station in Naples from the port then train out to Ercolano and a short walk to the site. We've been to both sites and in my opinion Herculaneum is a better one to visit.
7. If it's first time visit to Rome from the cruise I would do a ship excursion as it can be a bit daunting getting to Rome in your own. It can be done by train fairly easily but there are likely to be other ships in the port and train will be busy.