Restaurants in Rome +Venice with teenager who has food allergies
I think it is you who also asked this question on tripadvisor forums? The allergy cards are really the best way to go.
I don't think you will get any allergy-specific restaurant recommendations, you will just need to watch the food the teenager considers getting in restaurants recommended here (many here on CH).
Apart from the obvious usage of beans (fresh in season now) and nuts, I think the most tricky part will be avoiding the fats made from nuts (esp peanut) or seeds (esp. sunflower seed). For anything fried, ask especially insistently if any of those oils are involved.
There are some gelaterie that use one scoop per flavor and strictly separate the flavors to avoid cross contamination. Gracchi is the first that comes to my mind, but there are others.