Website disappears when changing permissions, unable to save edits in editor

I’m trying to get the security portion of my new website under control and decided to play around with permissions today. It’s a WP install on an nginx server.

I’ve changed all files to 644
All directories to 755
and wp-config file to 640

I’ve noticed when wp-config is on 640, the website no longer loads. I can’t view the website, or the dashboard. It only works when I set it to 644.

This second problem might be related and may help with troubleshooting. When in the WP dashboard, under appearance > editor, I can’t save any edits. I get this message on the bottom of the screen:

“You need to make this file writable before you can save your changes. See the Codex for more information.”

Is this a permissions problem, or a problem with my user account role?

It’s almost as if it’s treating my what should be an admin account as public. I’m sort of new with permissions and roles. Any advice would be appreciated.