1: Elena probably loves Italian food as much as - or more than - yours truly does
2: the amount of food per Italian-prepared plate is known (by me, at least) to "leave you wanting more", rather than making you want to throw up by the time you (if at all) manage to finish it
3: saying no to an Italian cook when offered [more] food is considered offensive
"Hunger has nothing to do with it. If there's food, you eat it. Italians don't make a connection between hunger and eating" (comedian Stephen Juliano)
If an Italian-american mother offers you food, accept it. Otherwise, she will just keep offering. She will not be able to relax, she will not be able to concentrate, until you are eating. So just accept what is offered, and every now and then touch a bite to your lips. That will be enough to keep her happy, or at least calm. I don't know what life is like in Italy, but this works in New Jersey.
I think it is a particular cultural heritage from people from south Italy. I'm from north Italy and I had some "problem" only when I was guest of south familys (I was a bad person to say 'no thank you' to an offer!). Anyway, It is very informal and impolite to say "I am full" because it a bad expression; we prefer to say: "Sono sazio" or more noble "Sono satollo"
This adjective is dependent on the thing it is modifying. In this case it happens to be the speaker (I am full) ... but if I say 'The dogs are full' it would be 'i cani sono pieni'. (I hope I have it right, this is my first lesson on pieni, but it seems to follow the same convention as the others.)
Same question I had, and I think I have determined that it really comes down to whether 'I' is female (piena) or male (pieno). If the statement is simply "I am full" then I think either one should be acceptable because you don't know the gender of the person making the statement.