I agree those, were the warm up questions and if Kate had, answered them there, would have been another 48..
She was absolutely right to answer none
You have inadvertently admitted the questions were of no importance
Angelo is correct, in a formal police interview situation a detective will ask a series of simple questions initially which should be easily answered. If the suspect hesitates or refuses to answer these innocuous questions then the police have the right to consider the witness hostile. At that point there is no point in proceeding to the more inquisitorial questions.
If the police have incriminating evidence at that point the suspect might be arrested and charged. If not they will normally be released while the search for such evidence continues.
I cannot understand your comment to the effect that
she was right to answer none. She was morally obliged to answer the police questions to the best of her ability, this was her daughter who had disappeared. The police were right in asking her finally, "Are you aware that in not answering the questions you are jeopardising the investigation, which seeks to discover what happened to your daughter?", to which Kate responded, "Yes, if that’s what the investigation thinks".
So my question is this. Why would the mother of a missing child refuse to cooperate in an investigation which has the sole purpose of finding that child?