Hi Dan, Resonar should by default display thumbnails on category archive pages, as you can see here on the demo:
https://resonardemo.wordpress.com/category/writing/
They are not displayed in a grid, however – for that, you’d need to make some adjustments with CSS, such as hiding the excerpt, moving the post title to a new position, and creating a grid layout. That would take some intermediate CSS skills to do. You would need to preface all your CSS declarations with .category if you only wanted to target the category page.
Don’t edit the theme files directly, otherwise your changes will be overwritten every time the theme is updated.
An easy way to add custom CSS is to install the Jetpack plugin and activate the Custom CSS module. You’ll then add your custom CSS in the new stylesheet editor that’ll appear in your dashboard, under Appearance > Edit CSS. You could also install a standalone custom CSS plugin if you prefer.