Hey aradiasun,
Thank you for your patience and the link to your example page. The page that you linked to is actually an archive category page, and not a post page, this is important because within WordPress archive page fetches “post entries” from the database with meta such as date, author, categories, comment counts, etc. but not the actual comments, so there is not a way to extract specific comments from these posts and display them in a specific order in your sidebar, in the same way you have the posts shown, unless there is a plugin that I don’t know about, which is possible.
But you can use the WordPress “Recent Comments” widget to display your recent comments in the sidebar, but I believe this is for all comments across your whole site and not specific to the category on the archive page.
Best regards,
Mike