March 13-15
I have to say that if you are in Venice in the first half of March you may be lucky but likely you will find it cold. Be prepared. I'd be more worried about that than an unlikely Aqua Alta.
A bit of clarification about transportation in Venice - there is a huge difference between a vaporetto and a water taxi. Both are boats, both are available at Ferrovia, the railway station. But there the similarity ends. Water taxis, as the name suggests, are private transportation for a person or a small group (up to 8) and their luggage just like a regular taxi in any city around the world. You tell them where you want to go and they take you there, or as near as they can, and then pay them - a lot.
A vaporetto (not vaporetti - that would be plural although vaporettos is often used in English for plural) is larger and the go-to public transportation for tourists and locals alike. Some of the boat is under cover, some inside a large cabin, and small open area at the stern. For 2 and a half days you could have 3 day passes which works out much cheaper than single tickets.
Gondolas are pure tourist, take 1 to as many as 6 but usually 4, human powered and slow, and generally go on relatively short set routes, and are expensive.
While a traghetto is shaped like an older gondola, it is all in black and has plain simple seats (the Venetian custom followed by many locals and few tourists is to stand for the duration of the crossing), is often worded by two men, and the crossing is very quick. The experience is nothing like a tourist gondola experience. They are now much more expensive than they used to be.
I don't see how you work out March 13-15 is 2 and a half days. Is the 13th the day you arrive from Milan? If so an hour or so doesn't count as a day or even a half day, So sleep in Venice 13th into 14th. The 14th is a whole day for sightseeing. Sleep in Venice 14th. Half a day of sightseeing on the 15th before you set off for the next destination? Except you'll spend part of that half day packing, checking out and putting the luggage somewhere to wait for you. I make it 2 nights in Venice and a day and a bit of sightseeing... have I got it wrong?
Venice is somewhat earlier for dinner time than many other Italian cities. By 10:30 even most of the pizza-by-the-slice places along tourist routes will be packing up, especially in March. Carnival will be over by 2 weeks and the city will be quiet in Lent. Maybe the McDonalds on Strada Nova will be open, but probably not - even it usually closes by 10. The idea of using the train as a dining room and packing a picnic is an excellent idea. It will be dark out so you won't be missing any scenery so you can give full attention to the food....
Part of the difficulty for first-timers trying to navigate around Venice in the dark (with luggage?) is that many of the quite common signs pointing you on your way are up high and yellow. And the lighting in Venice (I'd call it street lighting but there aren't streets) is somewhat yellow tinged so the signs kind of disappear. That may slow you down a bit. Best to have very clear directions and a good map.
