The anime was EXPLICITLY stated by DMC4 director Kobayashi to be canon, and since the anime references the first novel by mentioning outright that Dante once went by the name Tony in his youth, and the strawberry Sundaes, YES, the first novel is canon, Nell Goldstein made Ebony and Ivory, and Dante's modified them since her death. DMC3 never said he made them himself, only that they were homemade. I'd call Nell custom building them from scratched homemade.
And it has been confirmed again and again that Kobayashi don't have his **** together.