The dark-haired young woman in funeral clothes is Carmela.
Said young woman has been featured in both trailers so far, but Carmela has not been mentioned to be a part of the film, despite the fact that she and Tony dated in high school. Plus, Dickie is her first cousin, so it's not hard to believe that she would attend his funeral. Nor is it hard to believe that Carmela dyes her hair.- Jossed. A younger Carmela doesn't appear until later in the film, already with blonde hair.
Giuseppina is Christopher's biological mother.
Early in the film, Dickie mentions that Joanne is not able to get pregnant. If Dickie was able to get Giuseppina pregnant (which would be a victory over his father, since Hollywood Dick mentioned wanting a second set of children with Giuseppina), it's doubtful that she would want to raise a child, considering her professional ambitions and the stigma of being an unmarried mother in the sixties. Therefore, it could be arranged that Dickie and Joanne would take the baby and raise him. There's also the fact that Christopher looks more like Giuseppina than he does Dickie or Joanne.