I rent a cable modem from my ISP that has its own wifi capability. Does my ISP have the ability to track various settings on their modem, such as wireless network SSIDs, etc? Also, if I were to add an additional wireless access point, would my ISP have any visibility to the access point's settings?
Modern routers in their firmware have a setting to support CWMP (Customer-Premises Equipment WAN Management Protocol) for report management. This is also called TR-069 by it's name on Technical Report 069 as it first introduced. This capability is also called zero-touch configuration and most providers are now using for remote-configure your router.