Food on trains?

I'd get to the station early (are you leaving from Termini?) and pick up something there. You'll have MUCH to choose from, and probably better than anything which might be available on the train.

https://www.romatermini.com/en/store/index/food

I agree.
I've usually found pretty decent food, and wine, in European train stations. The choices on the train will be limited.

Those Frecciabianca trains do offer bar service, but I don't recall what food options were offered when I took that train. My guess is simple sandwiches and reheated pasta, along with alcoholic and non-alcoholic beverages. The sandwiches you can buy at shops in Termini will be better, so I too recommend buying your luncheon items before boarding. I'm pretty sure that's what I did.

And the cheapest bottled water anywhere is in the CONAD downstairs at Termini.

I agree with the others. Food on trains is not good, would only eat it if I were desperate. Much better idea to buy something at the train station, put together a picnic or whatever to take with you.

Are there any restrictions about a bottle of wine on the trains?

Nope, no restrictions on wine on trains.

You may get a round of applause if it's bubbly.

If you can, book seats with a table so you can spread out your moveable feast.

I've never encountered any restrictions on food or drink, including alcohol, on Italian trains. I've gone to the "dining" car occasionally. It's good if you want coffee; I don't drink it but there's always an espresso machine.

Caveat on the wine - either open it in advance or have a cork screw with you. Imagine the frustration of having a bottle of good wine and no way to open it on a 4+ hour train ride. Take plastic cups from your hotel bathroom.

I would carry my own food.

Buying food and drinks on the train is way overpriced! We always bring our own, including wine. Most other people do, too! That's what makes it fun!

While there are really no restrictions on food and drink, I usually open wine beforehand and stick to easy food items...not too messy, not too smelly, not enough room to spread out a 4 course picnic.

just don't let your fingers touch the food. Not classy in Italy. Use a napkin.