What is the reality and interpretation of an elderly woman's knowledge of future unseen matters through throwing date pits, knowing that she does not ask for money in return and only does it for relatives? Is this action permissible in Islamic law? And what is our duty towards her?

What is mentioned in the question is a type of divination and a claim to know the unseen. Her informing about what might happen is through jinn and devils who mix truth with falsehood. Her informing about accurate things does not indicate the validity of her claim or her righteousness, for the Antichrist (Al-Dajjal Al-Akbar) performs extraordinary feats, yet he is accursed. It is obligatory not to cling to the words of this woman or believe her, for whoever comes to a soothsayer and believes him has disbelieved in what was revealed to Muhammad, and advice must be offered to her.