You've done the right thing with Naples @Hosum . It's a bit of a "gritty" city, so if you are doing the transfer direct to Pompeii, it will no doubt pick you up right in front of the ship (there is a huge car park/taxi pick up zone right in front of the terminal). It's not somewhere I would like to go for a nice little wander, especially the port area!
I would recommend you get a tour guide to take you round Pompeii, you can ask when you are buying tickets at the kiosk, it's quite normal, and you will be added onto another group to make up the numbers. It's fairly reasonable price-wise, and makes the most of your visit. We've done both with/without a guide, hence my recommendation!
Barcelona has a blue tourist shuttle that takes you fron the ship to the bottom of Las Ramblas for a few Euros each, or just hop in a taxi, we found that to be approx same price because there is 5 of us.
Palma - I think a pp has mentioned that Cala Mayor is the next bay, and has a lovely beach with nice restaurants etc. If returning taxis are scarce, there are public buses that run right past the port entrance heading towards Palma. We normally dock at Porto Pi, which seems to be approx 2.5km from Cala Mayor beach, so not far at all.
Rome - the trains are cheap, but too much faff for us with luggage. We always book a shared transfer, but the drivers are absolute maniacs. Definitely book ahead for Colosseum. It's great skipping the queues. Plus you get free entry to the gardens that you can go later/the following day if that suits you better.
If you have booked a Guarantee cabin, the cabin number may be showing online now. Have a look on the app.