the isp issues you an ip
the router acts as a traffic cop directing traffic
with nat - it creates an internal network - subdividing the ip from the isp into its own network
dns - dynamic naming service
everything on the internet goes back to numbers
for convenience dynamic naming computers ( dns) are computers which translate those numbers into letters for you - its for convenience of users- if you remembered the numbers for say google if you typed those you would be directed to the site
usually people use the dns of the isp - you do not have to any will do
try open dns to speed your internet browsing speeds
http://www.opendns.com/
about the subnet mask
It was best described to me as blinders
For traffic that is directed internally in the network
- say you use msn messenger to transfer large files between computers on your network - handshake is done on the net , files are transferred though between the 2 computers within your home network at high speed - having those numbers of the subnet mask makes it quicker and easier to route within the router home network
lastly the dns is issued by the router by the dhcf service
Some of the time in setup you may turn it off
the router then acts as a switch only
networking people are the prima donnas of the computer world
they will not tell you much - too self important and busy
older networking books will tell and explain such things
useful site http://portforward.com/routers.htm