There's no particular need to move or copy any zlib files, just point the include and library directories to where they are in the source tree.
Most people won't have a hosts.ics file since they probably aren't using internet connection sharing.
You can get your computer's IP address by typing ipconfig at a command prompt, and if you need to know the external address of your router you can probably find it as the WAN address in the router config or you can visit
http://www.whatismyip.com/
If you do need to forward ports you should make the IP address on the server computer static so it doesn't change and break all your forwarding.