Una furtiva lagrima - score v. interpretation

Hi, I am learning Donizettis "una furtiva lagrima" from L'elisir d'amore, and I found that all the versions that I find on Youtube differ slightly at the end from the sheet I have . For one thing, the ending "si puo morir d'amor" is missing completely from my score, but that is probably just a matter of where you "cut" it. But what's more - on the last two "chiedo" the score says G, and Pavarotti gives us an A. Is this a usual way of improvising? What are the rules for declining from what the composer wrote? Teach a newbie, please!