Help needed on planning visit to Rome, Florence and Naples

You will be in Italy for five days from 3 Apr until 8 Apr.

I would advise you to spend you entire five days in Rome. I have been to Rome twice, spending a total of 10 days there and still have not seen all that I wanted to see.

The train from Rome to Florence will take about 1.5 hours, but just getting to the train station, etc. will use up about half your day.
Going on to Venice from Rome will take about 4 hours, so forget the day trip stuff.

If you resist my advise to stay in Rome, then you should limit your visit to no more than two days. If you choose Florence as your second city, then pick you days carefully there. The amazing Doumo (Cathedral) is not open every day. If you plan to see "David" at Accademia Museum, you would need to buy your tickets ahead of time.

Do some research on what you plan to see. TripAdvisor is a great source, keying in the city along with Things to Do.
Use Trentelia website for train tickets.
https://app.italiarail.com/results

First, go get a good guidebook such as Steves' Italy book. That will answer your question about what to see in various cities. Because of distance and time it makes more sense not to day trip to Florence or Naples. With five nights your really do not have time to see everything you listed. I would spent it in Rome and Florence and save Venice and Naples for another trip. Otherwise you will spend an enormous amount of limited time in trains and trains stations. Not a good use of time.

Welcome to the forum, Sudi.

In reality you have 4.5 days to play with as you'll kill the morning of April 3 dealing with flight arrival/immigration/and getting to wherever it is you decide to go first. As you've posted actual arrival and departure times, I assume you've already booked your flights and they're both in and out of Rome?

IMHO, I wouldn't take two of your 4 full days to day-trip Florence AND Naples. If you'd been able to book an open-jaw flight - meaning into one city and out of another - that would have eliminated the backtracking you're going to have to do from either place to Rome. As you're going to want to be in Rome on the end of the trip to make that 8:45 AM flight, you'll need to choose either Naples OR Florence and go directly there on the 3rd. Then take a morning train back to Rome on the 5th.

Or you could day-trip to one OR the other from Rome.

Or you can just spend the entire time in Rome. This is what I'd probably do as there's enough and more just in that one to fill your time. If you get bored - which is unlikely but could happen if Rome isn't your cuppa - then hop a train somewhere for the day.

Venice is too far from Rome to do on this trip without killing more of your short time in travel than I'd wish to. Florence is 90 minutes or so from Rome via fast trains from Termini, and Naples is a little over an hour. Venice is 3.5 hours.

What to do in Florence or Naples? Here's where a good guidebook is necessity so you can research and choose what appeals to YOU. You will want to take note of Sunday, April 7th: this is a first Sunday of a month when National museums have been free to visit. This is NOT a good thing where biggies like the Uffizi (Florence) and Colosseum (Rome) are concerned as they'll be mobbed so are best avoided. There is currently a question about whether free First Sundays will continue into all of 2019 but it may be up to the individual museums what they choose to do.