Both 32 bit and 64 bit Windows versions are fully supported. "Windows Server Core" is also supported - details. "Windows Embedded 7" is also supported - details.
(*) By "static" we mean an IP address which does not change, or only very seldom changes. It doesn't matter how the IP address is assigned to your computer/router (manually or dynamically). Many "always-on" Internet connections such as cable and ADSL connections provide an Internet IP address which never actually change even if it is supposed be be "dynamic". Such an IP address can be considered "static" and works fine for hosting domain names.
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