You can position the category links over the image like so:
.generate-columns-container .inside-article {
position: relative;
}
.generate-columns-container .cat-links {
position: absolute;
top: 20px;
right: 40px;
}
.generate-columns-container .cat-links:before {
display: none;
}
.generate-columns-container .cat-links a {
padding: 4px;
background-color: red;
color: #fff;
}
However, you’re images are not large enough to fit the columns hence the white space you have around them, in your current layout you will need that at least 540px wide.
Your footer meta needs to be set to include comments and date. And you will need to remove any custom functions you have added to remove the styling and layout of the meta.