You are correct that your router would assign IPs, subnets and default gateways via DHCP as your "main computer" would not have DHCP. You could assign static IP addresses if you had a static IP from your ISP. It can be done with dynamic, but it gets a little more complicated. Best to let DHCP handle it.
There are quite a few ways that name servers are able to resolve the queries. Recursive and non-recursive, etc. If you have a server that can act as a name server and uses forwarders, then your clients can send their queries to the name server which uses the forwarders to reach the local server on the Internet. This decreases traffic on the Internet and allows the central name server to build up a much larger cache of names than each local client. So, it is becomes much more efficient. Not to mention that once you put the DNS names from your ISP in as forwarders, you do not have to remember them anymore and can just point the individual clients to the server IP.
While this is more efficient, whether or not you would really notice a lot of increase in speed is dependent on the speed of your connection.
