Ah, I neglected to remove an important part from generate_posted_on().
Go into /inc/template-tags.php and find the generate_posted_on() function.
Then remove this from the top of the function:
if ( 'post' !== get_post_type() ) return;
That should display the date for you.
For the categories, I think custom post types use different functions to display taxonomy information, so you would have to add your own functions in there: https://codex.wordpress.org/Function_Reference/get_the_term_list