I am going to wrap up my comments in this thread with the following.
I regards to Eset new connection alert for your router. This is occurring because something changed its built-in MAC address. I doubt this is due to any anti-tracking mechanism built into the router. If this was the case, the MAC address changing would have been done once when the router fully initialized itself after setup or power up.
This leaves the conclusion that any attacker has access to your router. I would start by performing a hard reset on the router and change its Admin interface password to strong one. If this issue still persists, try to upgrade the router's firmware to the latest version that exists from the manufacturer. If the router is provided by your ISP, contact them about this issue and see if they have a new firmware version for the router.