Ok, for your router; double check, make sure you're getting the dns from your ISP, or set your router to send dns requests directly to your modem/gateway; 0.0.0.0 is a broadcast address; or in other words, every time you send a DNS request, it is broadcasted to basically everything. 0.0.0.0 is also used by DHCP; and it is possible to trick DHCP, into a VPN like state, so that does have me questioning, if your network could possibly have become a node in a zombie network...
Also, as for metadata; it depends, there are a lot of exploits, based on metadata, so it is possible. As for DNS exploits, there are tons of exploits there as well; most of the time though, people use DNS exploits in a sense of DoS, or to simply watch where you're going. Is it possible someone is trying to fuck with you, and make things difficult for ya; sure why not lol...
As for finding what's wrong; download wireshark, and monitor in promiscuous mode; this way you can see if there are any questionable connections, ect.. As for trying to get rid of it; make sure you're system is clean, use Avast for anti-virus, and also look up CCleaner (piriform), it works well cleaning out the registry, or invalid firewall rules. Change your router's passwords, and make sure it is set to only accept DNS from ISP; or get the DNS addresses from your ISP, and manually set it yourself...