I am not seeing the Related Posts widget in the sidebar?
This CSS will add an icon to the Categories list:
.widget_categories ul li::before {
content: "";
background-image: url(url_to_your_icon_image);
width: 15px;
height: 17px;
background-size: 15px 17px;
display: inline-block;
margin-right: 10px;
opacity: .5;
position: relative;
bottom: -2px;
}
You will need to upload your own icon image, and add the URL to where it says: url_to_your_icon_image
Once i can see the Related posts widget i can update the CSS to include that.