Welcome to the forum! I have a few thoughts on your proposed Itinerary and a few questions....
It would help to know if this is your first trip to Europe, and also where you're flying from? I'm assuming you're aware that you'll lose two days for flights, and arrive in Europe the day after you depart? It's great to see that you're planning on using open jaw flights.
My first suggestion would be to change the order of the places you'll be visiting. It's important to minimize travel times between locations, to allow more time at each place. Your plan to travel from the Cinque Terre to Venice stands out especially, as that will require the better part of a full day for travel, and several train changes. It's surprising that you're only allowing about 1.5 days for Florence, as there's a lot to see there.
In the same situation, I'd probably structure the trip somewhat like this.....
- D1 - Flight to Italy
- D2 / N1 - Arrive Naples, Curreri Viaggi coach to Sorrento (about an hour)
- D3 / N2 - Sorrento, day trip to Pompeii
- D4 / N3 - Sorrento, Amalfi coast day trip (if you want to see specific places, you might hire a private car service)
- D5 / N1 - Train from Sorrento to Rome (Circumvesuviana or Campania Express to Naples, high speed train to Rome)
- D6 / N2 - Rome, touring
- D7 / N3 - Rome, touring (you might consider a day trip to Orvieto, a beautiful hill town in Umbria)
- D8 / N4 - Rome, touring
- D9 / N1 - Train from Rome to Cinque Terre (use one of the fast trains to La Spezia Centrale, about 3H:45M and then the local train to whichever town you plan to stay in - plan for arrival about mid-afternoon - have you decided which town?)
- D10 / N2 - Cinque Terre
- D11 / N3 - Cinque Terre
- D12 / N1 - Train to Florence (trip will be 2-3 hours with one or more changes, depending on which train you choose and which town you're staying in)
- D13 / N2 - Florence, touring (as you don't know which "villages" you want to visit, one possibility would be a day trip to Siena by Bus, or to Lucca - you could also visit Pisa if that's important although I'm not sure it's worth the effort)
- D14 / N1 - Train to Venice (about two hours by high speed train)
- D15 / N2 - Venice
- D16 / N1 - Train from Venice to Munich (I'd suggest using one of the day trains, as it's a very scenic trip through the Brenner Pass - there's a departure at 09:10, arriving Munich at 16:26, time 7H:16M, one change at Verona Porta Nuova).
- D17 / N2 - Munich, day trip to Neuschwanstein Castle (you could certainly make the timed reservations and travel there on your own, or use a guided day tour with Radius Tours as they take care of all the arrangements and provide a guide for the trip down, but the official guides provide the tour within the Castle - be sure to make time for Marienbrücke to get the classic photos of the Castle).
- D18 - Flight home
This suggestion allows a bit more time in Sorrento, as you may need a day or two to recover from jet lag. I allowed four nights in Rome as there's lots to see there, and this allows time for a day trip. Unless you can add a few more days to the trip, you could cut one night from Rome and add that to either Florence or Venice. Depending on when you'll be travelling, you might find Venice is dreadfully crowded (also true of the Cinque Terre).
There are some potentially expensive caveats to be aware of when using public transit in Italy. Be sure to do some research on those.
As always, I'd suggest having a look at the Rick Steves guidebooks for the locations you'll be visiting, to plan sightseeing, hotels, transportation, etc. You should be able to find those at your local Library or larger bookstores.