The official inked certification suffices. Without that certification, it would not be an official copy.
Second, why is there no signature of the father???
Because the father's signature is not part of the official document. Father's signature is not on my 1966 Mississippi long form. Mine has mother, attendant, and registrar signature blocks.
Why is the mother’s typed name different that the signature? Wouldn’t she have had them type it the same way she was going to sign it?
The State of Hawaii doesn’t consider just a signature to be valid certification. The State of Hawaii requires the registrar’s signature AND a raised seal.