No. You only need this if your system shows "Windows 7" without "Service Pack 1" in System Properties.
Yes, for the 32-bit versions of those SKUs. windows 7 service pack 1 offline installer 32 bit
Absolutely. The file is digitally signed by Microsoft and does not phone home. It does not require an internet connection. windows 7 service pack 1 offline installer 32 bit
Introduction: The Legacy of Windows 7