Have you tried disabling the category-icons plugin? I think that’s what causes the error.
You add the code under Appearance > Editor > style.css
Just be careful not to delete any other code in there. To be safe, add it at the bottom.
home is a class of the body.
The correct CSS code should be this:
body.home{background: url('http://i1.wp.com/www.coreintentions.com/wp-content/uploads/2016/05/cropped-23-01.png?fit=250%2C70');}
I used your logo as an example. 🙂
You should probably check the correct prefix for the tables in your database. Once you know the correct prefix, open wp-config.php and update this variable $table_prefix.
Let me know if that helps. 🙂