How to create a clickable latest posts list?

I believe what you need is the wp_list_categories() function. You would need to do something like this;

    wp_list_categories( array(
        'orderby'    => 'name',
        'show_count' => true,
        'exclude'    => array( 10 )
    ) );

This will list all the available post categories ordered by title. You can have a look at the docs for this to find a list of all the parameters you can use.