I suggest that you install [FPW Category Thumbnails][1] plugin. It will cover every scenario mentioned in your question. It will save you from maintaining code in `functions.php`, and will do it visually! The built-in **FPW Post Thumbnails** will add very powerful styling to your featured images (borders, shadows, margins, backgrounds, etc).


  [1]: https://wordpress.org/plugins/fpw-category-thumbnails/