Does Windows 2K/XP support 64bit program?

The AMD64 and EM64T extensions are compatible. In fact, Intel licensed them from AMD.

As for the Windows Version, there is really one Windows 2000 version for 64bit CPUs. But it never left the "alpha" state and was build only for PowerPC as far as I recall, which is of course not compatible with AMD64/EM64T.

One WinXP64 final version was also leaked recently to the internet, but it had a bad crack, so it was "nuked" from all places you could get it from. But it shouldn't take long until it's available to everybody.