I think that wireless is fairly secure running wpa2 or wpa. And SO convenient. WEP however can quite casually be hacked by an expert running the right tools. If you don't need the wireless, disable it in the router gui. Basically if you set the wireless security to wpa on the router gui, you will just need to enter the password on the mac when you select the network. Hiding the ap doesn't provide that much security. They are still visible to a wireless sniffer when the network sends data. If you set a good password on wpa2, there are no current ways to hack into the network.
If the DNS is still the same after switching ISPs, it is likely that the MAC is still holding on to the old dns addresses. Perhaps they are hard set in the configuration, or the mac is using cached dns info from an old dhcp lease. The 192.168.1.0 network being the same could permit that. As you see, it still works. Most networks let DNS pass and anyone can use anyone's DNS server for the most part.
If you go into the router configuration gui you can see what your isp suggests to use.
I don't see the dns address in the logs, the 224.0.x.x thing is a multicast address, I imagine this is the mac setting up rendzevous, a cool protocol I don't understand. Multicast ispretty complex, but this is coming from the mac not the network.