I would like to remove the Author and Categories from the meta that appears before each post, leaving only the Date and Comments. I found this section of code in ./library/functions/functions.php but I would like to replace it in my child theme rather than editing this file directly. What’s the proper way to do this?
Yes, you can do through the child theme as you will not lose the changes while updating. It is the best way.
But changes that you want to make is very small change for which you do not need to make child theme. You could write custom css these changes will still remain if you update also so no worry here also.
Go to Appearence->Theme-Options->Design Options->Custom CSS Paste the following CSS and click on save all changes.