Router login troubles R7000

AP stands for Access Point. It's the part of the router that provides Wi-Fi services. Many of the basic router functions are disabled when a router is running as an Access Point. The firewall separating the Internet and LAN ports as well as the DHCP server are disabled, among other things. 

I was speculating that your R7000 was set up to run only as an wireless Access Point. The reason why I suspected this was because you were able to connect to it using a public IP address. This is not definitive proof that of the router running in AP mode. But you can see for yourself by logging into the router and going to ADVANCED > Advanced Setup > Wireless AP. There, you will see whether AP mode is enabled.

Even if it's not enabled, a factory reset may be good medicine to clear out any potential funkiness going on with your router. Maybe you inadvertently purchased a customer return or a refurbished unit.  Or maybe you got a brand new unit that was not properly set to factory defaults at the manufacturer.