How to display category list with category description

Use this instead of wp_list_categories( $args );

wp_list_categories( $args ); 

It will display the category with formatted results like <ul><li>

$categories = get_the_category();

This will returns the all category assigns to the current post and store in $category variable.

Then you can display as in you listed format

$page_custom_image = get_field("your_custom_field_name", "texonomyname_" .$category->term_id);