I tried PSDK Feb 2003 downloadable from
http://www.microsoft.com/msdownload/platformsdk/sdkupdate/psdk-full.htm
and this two issues went away.

>- When WINVER is set to 0x500, vc6 gives a long warning because at the
>time, windows nt 5.0 was only at beta stage. Moreover, there are other
>clashes between winsock.h and winsock2.h, that show up when WINVER is
>0x500.

Next, I tried to compile Modules/socketmodule.h's _MSC_VER >= 1300 part
but this didn't work.

#if _MSC_VER >= 1300
# include <winsock2.h>
# include <ws2tcpip.h>
# include <MSTcpIP.h> /* for SIO_RCVALL */
# define HAVE_ADDRINFO
# define HAVE_SOCKADDR_STORAGE
# define HAVE_GETADDRINFO
# define HAVE_GETNAMEINFO
# define ENABLE_IPV6
#else
# include <winsock.h>
#endif

I didn't investigate too much, but it seems
#include <windows.h>
#include <winsock2.h>
causes another conflicts between winsock.h and winsock2.h
this time.