All comments follow the content, not the Publication or Niche, so any comments made will display any place that the content appears. However, if the content post is owned by a Publication, the editors and admins can delete comments as they control their brand. However, if a comment is deleted by the Publication, the commenter does not go conduct negative under that action.
All comments, whether on a Personal Journal, Niche or Publication are still subject to rejection for AUP violations. Comments that are flagged and subsequently removed for AUP violations result in reputation penalties and the offender becomes conduct negative.