If you froze the Kingo SuperSU before replacing it with the Chainfire/Codingcode SuperSU, try going through the entire process again, but with the Kingo SuperSU running. Go into it's Settings menu and disable its functionality, And this part applies to any app you want to completely remove all traces of if, when you're uninstalling an app, don't just tap the 'Uninstall' button. Tap the 'Force stop' button, now tap the 'Clear data' button, and then the 'Uninstall' button. If you don't 'Clear data' a lot apps leave their settings and config files behind when you tap the Uninstall button. Now be sure to go into the Settings menu of the Chainfire/Codingcode SuperSU.
It's not a matter of every app having root access. Most do not, as that's determined by the developer of the app, SuperSU cannot enable/disable any app to have root access, what it does is do is allow you enable/disable root access for those particular apps that are 'root' capable.