Ok for widgets you have to add your registered Custom Post Type on query codes. On Theme Directory/inc/newscard-widgets.php file, you can find the below code on line no: 195, 361 and 483.
'post_type' => array('post'),
to the mentioned code you have to add the registered Custom Post type as
'post_type' => array('post', 'your-custom-post-type'),
and to add taxomony (custom category) on dropdown list you have to add the taxomony on dropdown query code. you can find below code on line no: 169 and 335.
'selected' => $instance['category']
add the the taxonomy query code just beneath the mentioned code followed by comma (,) and after adding the code should look like this.
'selected' => $instance['category'],
'taxonomy' => 'your-custom-taxonomy'
We haven’t tried instantly but hope it should work and if it doesn’t work you for you then i think you have to hire a developer who is more familiar with the codes and can customized the Theme code for you.
Thanks