1. Which is the best operating server system for AC, windows server 2003 or 2008?
2008 since 2003 really isn't supported by M.S. or won't be much longer.
2. Is it true that AC will not work is a domain server.
I am currently running AC 6.1.2 on my domain server and there is no problem.
64 bit totally works fine in AC.
the practical advantage of 64-bit is that it allows you to have much more RAM. Instead of the 4GB maximum in a 32-bit machine, you can have seemingly unlimited amounts.
For example here are some RAM limits to different 64bit O.S.
Windows 7 Professional, 192 GB
Windows 7 Home Basic, 8 GB
Windows Server 2008 R2 Enterprise, 2 TB
Windows Server 2008 R2 Standard, 32 GB
see the full article on RAM limits here