Is it a good way to travel from Venice to Rome by night train?

Tiburtina station is on Metro line B, so it's an easy connection from there to other parts of Rome. Depending on where you're staying, it may be necessary to change to Metro line A or a bus at the Termini station stop.

Thanks. Do you know if I can take subway with suitcase? Also do you have idea how much do Taxi charge from there to Fiumicino Airport

There is a dedicated shuttle train, the Leonardo Express from Rome's main train station (Termini) to Fiumicino. The trip takes 1/2 hour and cost €11.

Also, it is only 4½ hours by train (Italian Eurostar) from Venice to Rome Termini.

Thanks. My flight time from Rome Fiumicino airport is 7:20 am. I am afrid that the shuttle train won't be good for me. I should be airport around 6:00 am.

By law, taxi fare from Rome to Fiumicino is 40 Euro, luggage included. Taxis are normally allowed to charge a supplement of a couple of Euro for trips between 10 pm and 7 am, but I don't know if that applies to the airport run as well.

What night are you taking the overnight train on Warren?

We may be taking it the 19th to arrive morning of the 20th.

My plan is taking May 17 evening train (23:30pm 771 Marco Polo) from Venice St. Lucia station to Rome.

With a 7:20am international flight out of FCO, don't plan on taking the Leondardo Express. They don't begin their daily runs until about 5:50am. You get to the airport at 6:30am. You really need to be at the airport 2.0hrs-3.0hrs early for an international flight. Terminal 5 can sometimes be an inefficient zoo. Your hotel can have a taxi waiting for you very early. It's done all the time.