Yes, the fish is Barovier & Toso. I would love to put it in the Murano Zoo, Michael. If you would like to have it in the zoo, just email your full name to me and I'll give you credit.
Your fish has perfect examples of the eyes Barovier & Toso were famous for. The look like glazed black pupils on white glass. I don't know how they achieved the look, but it gives so much life to the animals that have eyes like this.
As for graffito -- there are several different looks to graffito, so I wouldn't want to say yes or no. It is not fenicio, though. Fenicio is applied to the surface, then combed. From what I've seen, the fenecio decoration is sometimes left on the surface or it can be cased. The canes in this fish look more like are formed and suspended in the glass to me.
I am open to what graffito is. Fratelli Toso graffito looks like random canes snaking around inside glass. Some looks like spider webs. Others look like the duck in the link. What makes something graffito, I don't know. And anytime I talk technique, I wind up in trouble.