Hi again,

#1. To change the background color for Blog Overlay, please add this custom CSS to file style.css ( child-theme):

.post-style-3 .post-inner .post-thumbnail:before{
background: rgb(your-color) !important;

#2. I have corrected the display image to full-size for you, however, because the featured image and the displayed blog image have different sizes, it will be cropped to fit the display layout.