What is the ruling on writing a document for the police and competent authorities to testify to the husband's innocence in the killing of his first wife, and is it permissible to sign it? And is it permissible to sign a similar document for the family of the second wife?

You are permitted to testify to a person's good character, so long as you know them to be so. However, your testimony may not be beneficial if there are strong circumstantial evidences indicating that he is the killer. This is referred to as "lawth" (a strong presumption of guilt) by the jurists, and it is what justifies the blood relatives' demand for their right. Jurists have differed on the definition of lawth. In the event that the crime is not proven, your testimony may be beneficial in preventing the authorities from imposing a discretionary punishment on him. It is advisable to urge the blood relatives towards reconciliation, acceptance of blood money (diyya), and forgiveness, for Allah Almighty has commanded and encouraged reconciliation and forgiveness.