How do I check what DNS server I'm using (on Mac OS X)
You could try issuing the following at the command line:
scutil --dns | grep 'nameserver\[[0-9]*\]'
It should give you a list of DNS servers configured on your system.
Your router is acting as a DNS forwarder, you ask your router and your router asks a DNS server for you. You need to login to your router web config to figure out what it's using, or you could just enter it directly into your Network configuration.