I can't help with the mirroring issue, but I can clear up any confusion about the IP addresses. What you're seeing implies both devices are on the same network. There's four numbers comprising an IPv4 address separated by periods. For simplicity, the first 3 give the network and the last is unique to each device on the network. For example, two devices:
192.168.0.45 and 192.168.0.100 - same network
192.168.1.45 and 192.168.0.100 - different network; won't be able to communicate with each other
In addition, depending on router settings wired devices may be able to communicate with each other while wireless devices cannot.
Since you say your other home devices can connect to each other I assume some if not all are wireless, so it's probably not a router issue. Maybe someone else has an idea. Maybe a phone setting? I know use of a VPN on a phone can mess things up. I've had little to no luck with mirroring, but I have nothing Apple.
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