Any computer that connects to the same router, will be connected to the SAME network. WIred or wireless, they are the same!
So setting up a server is simple. Just set up a server. It doesn't matter how you connect to the router. The server will need to be setup properly as well the laptop but it will still work just fine. So forget about connecting directly with a cable you ARE CONNECTED!
You may need to better understand how a server and a network works to get all of it working, but the connection to the router is not the problem. If you want the SERVER to issue the DHCP addresses, turn off the DHCP on the router let the server issue the addresses. You can only have ONE DHCP server. Even if you let the router issue the addresses its not an issue.
--Edit--
Unless your ROUTER has a client mode (most do not) then it can not be used as a wireless bridge. There is no way to tell it to what SSID to connect into. Some routers have WDS modes which could be used to connect two routers together wirelessly as well. Unless your old B router has one of those two items, you will need a different device - like a wireless adapter, wireless bridge, etc.
Running a server on a wireless device is not a good idea, just for information, it will work but it will also be very sporadic in operation.