You can use the [show_post_snippets] shortcode (pls see documentation on this and use post_type as course and taxonomy as course_category) to display courses pertaining to a certain category.
Another way – if the data is not changing that much, you can even create web pages using the HTML generated by these category pages that you already have access to. When the course changes you may need to redo the HTML.
One last way if you want to change the course_category pages, you can change loop-course.php file to include category description as part of content (at present, it shows up on the top of the page below the title). Pls add the following code and something similar to line number 43 of loop-course.php file –