Is there a way to override files form the layouts/joomla directory? I need to change the look of the Read More button. Found its php in layouts/joomla/content/readmore.php. Could I copy this file to my template folder and change it?
Yes, absolutely. You can override the layouts by copying the file to
templates/YOURTEMPLATE/html/layouts/ using the same path as where you found the file.
So in your case, copy the file currently at