Why do they install Windows 2003 on the operating computers and Windows XP for the administration in Networks?

windows 2003 is an edition for servers. The computer doesn't really run (or has to run) on the computer itself but on a server. The computer that administer this network can't run on itself ofcourse. If something would go wrong with the server, and the administrating computer uses windows 2003 (so it needs the server to start up for files, or runs totally on the server) you can't even acces your server and wont be able to fix it. Therefore it needs to be able to run on itself: windows xp.

Why windows xp and not windows 7? I think it's a personal choice. Windows xp is more "tested". Windows 7 is newer and therefore riskier.

I am not sure, but no, you can't install the server on 5 pc's...you can only use the cal for 5 pc's, the cal license is something different that the server license.

windows 2003?????

i guess you mean something esle??

usually a network needs same operating systems to avoid conflicts