display all categories

There is WPDM Categories widget. You can use that one to show all Download Categories.

Can it use shortcode to show all categories or specify category id in a post or page?

You can check Extended Shortcode addon. It has [wpdm_tree] shortcode, which shows all categories in a tree format.

And WPDM Directory addon has the multiple category shortcodes. Demo of WPDM archive page category shortcode (https://demo.wpdownloadmanager.com/wpdmpro/categories/) Check other shortcodes too.