1. Is it possible to show “0 comments” instead of the “Leave a comment” text (https://imgur.com/KBscvz9)?
It should always show the post’ comments count: In case the post has no comments yet, it should show “0 comments”. Otherwise, it should show “X comments”.
Regarding your first answer, I tried the generate_leave_comment filter using the snippets plugin but it’s not working. The two filters Tom suggested the other day work pretty good but not generate_leave_comment. I can’t change the default Leave a Comment text.