So I have an amazing theme IMHO, called Avada from Theme Fusion. However, the WordPress theme doesn't come with a way to edit/design the category page, so the blog category pages look like crap.
Any suggestions on this?
First, if you are going to add to the theme, learn about Child Themes https://codex.wordpress.org/Child_Themes .
Then, create your own Category page - use a copy of one of the templates in your theme (placed in your Child Theme) and adjust the query to do a category-type query.
By creating a Child Theme, you ensure that any enhancements you make to the theme are not overwritten with a main theme update.
You might also be interested in the Template Hierarchy, which is how WP selects a template for various types of pages. Start here: https://developer.wordpress.org/themes/basics/template-hierarchy/ (within the Theme Handbook, also a great learning resource).