Fancier Author Box comes at the end of the_content function and related_posts always come after that, so it's not possible to do this.
The premium version, Fanciest Author Box, does have a shortcode and a template tag which would work for you, but that's a different story.
You could try inserting related posts into the_content function and then
add_filter( 'the_content', 'ts_fab_add_author_box', 1000 );
Regarding the css changes you made, no problem, you can alter it any way you want. We also plan on implementing an option of hiding that "recent posts" tab in one of the future updates.