Train Tickets

I'd wait on the May 12 ticket since you could get delayed along the way. When you reach Rome you can make a decision about whether it's worth it to you to pay (probably) the full fare of 48 euros to take the fast train to Naples or you're willing to spend an extra 1 hour or more in transit on a slower train. I'll let others address your detailed questions about that day.

Fares on the Freccia trains from Naples to Rome seem to range from about 20 euros (non-refundable/non-changeable, probably needing to be bought well in advance) to the aforementioned 48 euros. There are many fast trains every hour, so unless there is something unusual about the date you are traveling (holiday, etc.), I don't think you need to be concerned about a sell-out. And all the fast trains probably won't be as expensive as 48 euros, based on what I'm seeing for today's and tomorrow's trains. Why don't you take a look at the May 17 fares shown on trenitalia.com every day or two. As long as you continue to see lots of trains at attractive times at prices you'd be willing to pay, you can let it ride. Once you're sure of your timing, you probably will save some money if you go ahead and make the purchase.

The Rome-Venice trip on May 21 is potentially going to be rather costly if you don't buy the ticket in advance. It's a 3 hr. 45 min. trip. I see prices on some May 21 trains below 40 euros at this point. The base fare (what you might pay at the last minute) seems to be 87 euros. So this is the ticket I would be most interested in purchasing in advance. There seem to be about 2 Freccia trains per hour running between Rome and Venice.

a. Do not buy advance tickets because you cannot be sure your plane will land on time. From Ciampino airport you take a bus to Rome Termini station. A full fare ticket bought at the station is 48 EUR pp for 2nd class high speed train with Trenitalia, or 39.90 EUR for a 2nd class high speed train with Italotreno. That is to Napoli Centrale. Then walk to the Circumvesuviana platforms and buy tickets to Sorrento. They are commuter trains with no advance purchase discounts.

c. an d. You can buy advance tickets from either of these 2 operators and save money with nonrefundable tickets. Just pick a late morning time. Time to get up and have a relaxing breakfast, then a relaxing trip to the train station. If you arrive at your destination too early you can't get into your hotel room. Also early morning and late afternoon trains are more expensive because that is when business people like to travel.

European trains rarely sell out, adding cars to a train is easier than adding seats on a plane.

In Italy it can happen in August and before/after Easter Monday. The trains going from the big cities to the seaside villages can be very crowded during the summer week-ends.

People reccomend to get tickets in advance because discounted tickets are not available for sale on the day of travel. The problem is that discounted tickets are also restricted: they can't be changed or refunded. If you are not interested in saving money, you can buy the full price tickets at the counter up to 15 minutes before the departure.

Even full price tickets are wasted one hour after the departure of the booked train.

You'll have to take a bus or a taxi from Ciampino airport to Roma Termini station.

Trains run frequently on these routes and pretty much never sell out. You can buy on the spot in stations, or a few days earlier if that's when you're ready to commit. Rome to Venice is obviously the longer, more expensive route, so advance booking saves more money there, versus a full fare of about $100 per person in the cheapest class of service.

Ciampino town has train service (connect by taxi or 1-euro bus from the airport), or the airport has direct SIT shuttle bus service to Roma Termini. Summary at https://ciampinoairport.net/rome-ciampino-airport-transfers/bus/#/search.

You can wait to buy tickets in Italy either on your day of travel or shortly before. The high-speed trains will be more expensive if you wait, but you gain flexibility. Both Trenitalia and Italo run high-speed trains on the routes you mention, and discounted tickets are available up until the day before unless sold out. Italo often has discounted tickets available after Trenitalia's discounted tickets are sold out, so don't overlook that option if you can commit to a travel time at least one day in advance. The local trains between Naples and Sorrento are operated by a different train company. No discounts are available and local trains won't sell out, so buy those tickets on your travel days.

You will need to go to Roma Termini to catch the train to Naples, There is bus service between Ciampino airport and Roma Termini, and hopefully others will know about other options. For example, there may be a fixed fee taxi option.