Hello David!
You are correct on your first point. The privilege exec level x cmd command is used to set the minimum privilege level required to execute a command in exec mode. On the other hand, ‘privilege configure’ is used to set the minimum privilege level required to execute a command in configuration mode.
Now the behavior of your scenario is quite interesting. I recreated it in the lab and confirmed this behavior. The command show running-config is indeed allowed, and you can see this because you don’t have an error message stating % Invalid input detected at '^' marker. The command has run successfully, so your privilege configuration is correct.
The reason you see no output is that while the command is recognized (and not invalid), the device’s security settings prevent the display of configuration details at that current privilege level. It’s a security measure to prevent unauthorized viewing of sensitive configuration details. So the privilege level doesn’t have the necessary rights to output the config file info on the screen.
I did some further experimentation and found that even privilege level 14 does not display the running configuration information on the screen. Only level 15.
I learned something new today! 
I hope this has been helpful!
Laz