As a person that also lives in northern Italy, and that have a girlfriend with a series on food intolerances, I can confirm with what OP already said. If you are celiac you can find options now days (obviously much more if you live in a city). If you are lactose intolerant you can also find options (Italy is also a place where lots of cheese is consumed, and many recipes involve some kind of cheese or cream). If you are both at the same time, well that’s where problem starts appearing.
If by any chance you also got a vegan in the group well it’s better to just cook yourself (obviously exaggerating but still your options of places may be very limited).
All this to say: you can find options now (when I was a kid it was unheard of), either with big restaurants/pizzerias that have a double kitchen, or with dedicated places that are fully gluten free.
Yes, because I find hard memorizing a lot of symbols before becoming capable of minimal reading proficiency.