Is it permissible for my father to deal with a person who claims there is a treasure of gold guarded by a jinn, and also to deal with shaykhs who demand incense to extract this treasure? Is it also permissible for him to deal with a person from Togo who claims to possess 300 kilograms of gold and asks my father to find a buyer from Saudi Arabia? And would I be betraying a trust if I informed my mother and siblings of this secret that my father told me?

We previously explained the prohibition of seeking help from sorcerers and jinn to extract treasures. As for your question about buying gold in Togo, this falls under commercial brokerage (simsarah), which is permissible in principle. However, it is a condition that the broker's fee (ju'alah) be known. It is not permissible for it to be a percentage of the sale price if it is unknown to both parties at the time of the contract. It is also a condition that the sale itself be Islamically permissible. As for revealing your father's secret, the general principle is that a secret is a trust that must be preserved, and revealing it is a forbidden betrayal.