Yes, yes and yes.
Book is a whole different thing. It's a very intricate jewel of writing, where you've got themes ranging from Voltaire, through Conan Doyle to One Thousand and One Nights with religious debate, Aristotle and medieval setting overlayed on top of everything. (Like other Eco's books it's very postmodern in that aspect)
Therefore it isn't surprising that movie didn't have too big ambition of being the book but just focused on the gust of the story and was very competent in that regard. But that's precisely why someone who did love the book might hate the adaptation. I didn't. I did enjoy both, although on entirely different levels.
You should definitely read the book.
Did you read Baudolino? It's Nameoftheroseish in many aspects and I guess you're going to like it. I've read it back in high school and ever since I wanted to pick it up again.
Eco is Italian and from what I recall all his books are too.