Is there any assurance in canon whether or not all trolls have belly buttons, or is the lack of them fanon? What about the hole in Kanaya's stomach that the fandom sometimes calls her "belly button"; is that a joke based on what went down between her and Eridan, or does she actually have a large hole through her abdomen because troll anatomy?

Trolls should not have bellybuttons since they hatch from eggs. And whether or not the hole in Kanaya’s torso has healed or not has yet to be seen or mentioned.