The OS isnt tied to the case. You really need to check on Wikipedia for some information about what a OS is and that. If you plan on building you really should know a bit more information.
The OS is the software that runs the computer. No one ever said you had to pay for it. There are Linux distros out there for free. Just have to download, burn and install.
IF you want Windows then yes you have to pay for it.
1 PC = 1 copy of windows.