Child theme question for SOCIAL theme

I’d like to make some modifications to Social. Specifically:

when you go to a category archive:

http://lamsocialclub.com/category/articles/

– I’d like to only show the publish date if the post is not an Event category post.

– I’d like to add a shortcode so that if you’re logged in, you see the text

– make modification to the header navigation

– and a few others

My question is, do I just copy the files from the parent theme that I’m going to modify and put it in the child theme folder with the same hierarchy? Is that enough?

Do I create a new functions.php file for the new functions or copy the functions.php file from the parent theme, and add the functions to that file?

Thank you,

Giovanni