I've only traveled solo in Italy, so I don't know from experience about splitting dishes, but I've read here and there that it's frowned upon in some places. On the other hand, I've never had an issue with ordering less than a full meal - maybe just an appetizer or soup and a main course or a pasta course. If you are wine drinkers, you can get house wine (usually pretty good) by the carafe in various sizes and share that. You can also share bottled water in a restaurant. While tap water is usually very good in Italy, it can be a challenge to get it in a restaurant. I don't usually eat dinners in Venice. You can easily fill up on cicchetti (the Venetian version of tapas), with drinks, of course, by visiting 2-3 bars in the late afternoon/early evening. There are lots of restaurant options in Rome and Florence for dinner. I usually grab a snack or pick up something at the nearest mini-supermarket for lunch. You'll find lots of gelato even in the height of winter. And there's always a place to stop for hot coffee (and some places for hot chocolate) and people watching.
In Venice you either walk or take the vaporetto. Single rides are expensive but you can buy a pass for the time you are there and ride as often as you like. The passes are for 24, 48, 72 hours - depending on how long you'll be there. Riding the vaporetto up and down the Grand Canal, especially very early in the morning and late in the evening is magical. You can walk to nearly every sight in Florence from the center. One hopes that your agent has booked you into a centrally located hotel. In Rome, you'll need the metro and/or bus and/or taxi to get around as it's much larger and the sights are spread out. As acraven said, the metro is simpler, but some buses are pretty easy to find and taxis are everywhere (insist on the meter).
In Venice the Secret Itineraries Tour of the Doge's Palace does indeed need to be pre-booked as there are only a couple tours a day and in small groups, so they sell out. I found the tour very interesting. You will be taken to parts of the Palace that are closed off to general viewing. Before and after the tour, you'll have free access to the rest of the Palace. A few people have reported back that they really liked a gondola rowing lesson and it's cheaper than a gondola ride.
Weather in March is unpredictable. I've been to Venice twice in February and both times had at least one rainy day and one sunny day. I've been to Rome twice in February, the first time I had mostly sunny days and was happy to shed my jacket in the afternoons. The second time, it snowed (albeit the first time it had snowed in Rome for some 25 years). Even then daytime temps were above freezing and after 2-3 inches of snow fell at night, the next day was full sunshine, not a cloud in the sky (and some fun photos). Whatever winter outer clothes you need to get to/from the airport at home will probably be enough for Italy. Layers are always recommended. If not in Venice, in Florence you'll be able to get good warm Italian leather gloves and warm scarves and hats in and around the market. I'd take one pair of comfortable water-resistance shoes and warm socks. I have no idea what ankle booties are, but whatever shoes or boots you wear during the day you can wear to dinner. I would only take evening wear if I planned to go to the opera - and probably not even then. I always take a good quality rain poncho. I prefer that to an umbrella in the rain because [1] it's less weight and bulk to carry around than an umbrella, [2] it keeps my hands free for taking photos and other stuff, [3] it covers my day bag, [4] it keeps more of me dry than an umbrella.
Blend in - sure, you'll blend in with all the other tourists :-) All the locals will know you're tourists no matter what you're wearing. There's no shame in being a tourist.