RelatedContent and similar parts (SnComments) cannot work in standalone mode - they need to be attached to the parent part (blog, discussion topic, or your custom parts). As Kristijan said, there are two properties that control their behavior, ParentEntityId and ParentEntityType. For example, if you want to attach a related content to the blog post, you would write something like this:
relatedContent.ParentEntityId = post.Id;
relatedContent.ParentEntityType = SnEntityType.BlogPost;
Where relatedContent is your Web part, and post is a blog post entity.