welcome to the forums. I've lived in Rome for 35 years though I'm American, or I should say, Italian-American. Growing up there in an Italian-American context, I thought I was Italian - until I came here and found out just how American I am.
Italian -American cuisine is very different from Italian. Though some of the immigrants maintained their traditional dishes, like my family made tordelli with 3 kinds of browned meat, onion, spinach and cheese all in the same filling, as it was made in Barga (prov. di Lucca) where they emigrated from, but made lasagne with a layer of ricotta and no bechamel - i presume because lasagne was not a dish they made in Barga in those days (no one had an oven) and they picked up the italian-american version from their friends. No doubt the lasagne with ricotta was typical of some other small town in Italy and caught on in the states for some reason. I've often wondered where this came from. Maybe you know? Certainly not Bologna. My Italian mother in law from Pontecorvo (Lazio) would put bechamel, plain tomato sauce (napolitan ragu) and sometimes little meatballs in a layer (probably influenced by timballo) in her lasagne and she never made any dish that was not part of her tradition - never used a cookbook, and made a very limited number of dishes, always in the same way. Probably there are a hundred varieties of lasagne, though everyone seems to consider Bologna to be The lasagne.
(My husband used to want to get of the train when it would stop in Bologna and run out to one of the people selling trays of lasagne on the platform because it was so renowned. The train would stop only 5 mnutes on the platform! I'd go crazy thinking he wouldn't make it back, but such is the appeal of Lasagne Bolognese!)
Anyway, I have no problem with putting cheese on fish pasta if it seems good that way, or of having pasta on the side or as part of a chicken dish (Chicken Tetrazzini - invented in America for the wonderful soprano Luisa Tetrazzini.) as long as it tastes good.
Americans like chicken in everything, it seems, and though I do recoil at the idea of chicken on pizza or chicken in a tomato sauce, i do love chicken tetrazzini. Traditional dishes are great, but i also like to try new things - for me, that's the whole appeal and art of cooking.
Anyway, it will be interesting to see your take on things, because you'll find that Italian food is very highly considered and lots of people want to know how things are made traditionally.