I’m not totally sure I’m following this topic. The WP Editor is just a 3rd-party plugin that makes code a little easier edit from your WordPress admin panel. But I can see your custom.css file is empty:
I think this more of a question for the people who make the WP Editor plugin, right? You’re basically just trying to get your code to save to your CSS file located in your Child theme and you can’t? I’m honestly not sure on that one unless your files in your Child theme folder aren’t writeable on your server. — http://wordpress.org/support/plugin/wp-editor
Also, you don’t have to use the editor in your WP admin to edit the files if you don’t want to. You could also edit them locally on your computer and update them on your server with an FTP program. This is probably more ideal than through the actual WordPress admin panel. I really only show that plugin in the video because it makes it easy to show people the relevant information without having to teach about unrelated topics like how to upload files to a web server, etc.