Hi There,
Thanks for writing in!
To add the social icon in the header widget area, you have to add custom HTML widget and following code to the text widget.

<a href="https://www.facebook.com/ThisIsPhillipIsland/" class="facebook" title="Facebook" target="_blank"><i class="x-icon-facebook-square" data-x-icon="" aria-hidden="true"></i></a>
<a href="https://www.instagram.com/thisisphillipisland" class="instagram" title="Instagram" target="_blank"><i class="x-icon-instagram" data-x-icon="" aria-hidden="true"></i></a>
<a href="https://www.pinterest.com.au/thisisphillipisland/" class="pinterest" title="Pinterest" target="_blank" style="outline: none;"><i class="x-icon-pinterest-square" data-x-icon="" aria-hidden="true"></i></a>
I would suggest you to add the social icon in header bar instead of header widget. to do that lease go to X-Theme Option -> Header -> MISCELLANEOUS section you can active the top bar and it will automatically show the social icon.

For the social share icon below to the post content, you have to use any social sharing plugin for that.
You can check this too https://wordpress.org/plugins/ultimate-social-media-icons/ or you can explore more in the plugin directory.
Hope this helps!