1) I've always wondered what possessed Michael to tell her that story in the first place. That's a private, family story that implicates his father in crime - and he's telling it to an outsider? I get that she's his girlfriend...but still.
It made for a good scene near the beginning (note the expression on Kay's face), and a good opportunity to introduce us to how Vito got things done in his world. The novel states that Michael was trying to gradually introduce Kay to his family background--she'd have to know those things sooner or later.
