When Jack is eating dinner with the priest, music from Madama Butterfly is playing in the background. Mathilde and Clara's nickname for Jack is Mr. Butterfly.
Violante Placido is the daughter of Simonetta Stefanelli who, as Apollonia, stunned Michael Corleone, in The Godfather (1972) some 40 years before this film's similar American-hiding-in-Italy was stunned by her daughter.
They called the rifle a Ruger M14. The M14, an infantry rifle in the 1950s, was not made by Ruger, and shoots a .308 (7.62 X 51). The correct rifle is a Ruger Mini-14.
When Jack and Mathilde go to the river to test the new rifle, she asks, "Muzzle velocity?" Jack answers, "About 360 miles an hour. That's including about 20 miles an hour off with the sound suppression." A ballistics-savvy person like Jack would have answered in "feet (or, meters) per second."
When Jack receives the Swedish newspaper clipping the text following the headline has several grammatical and punctuation errors indicative of it being written by someone whose native language is English. One of several examples from the article is that in Swedish homicide investigation is a single word - "mordutredning" - not two ("mord utredning").
She wasn't. She was killed because the gun Edward made for her, exploded in her face, as intended by Edward. Remember he made some last minute modifications just before delivering the gun.