Are you the only author on the site? If so you can just add this:
<?php magaziner_social_links() ; ?>
In single.php on line 45 with a child theme, after where it says:
<p class="bio-desc"><?php the_author_meta('description'); ?></p>
If you want different social icon links for different authors, then you would have to look at a plugin, as that requires new admin fields etc.
As for the author image on author archives, I just haven’t included it on my themes. Perhaps something for a future update.