Is what the sister claims – that a sign descended from the sky bearing the Beautiful Names of Allah after her supplication, and that she knows what goes on in their homes and foretells what will happen to them – possible, or is it a psychological condition?

It is most probable that what the sister is suffering from is satanic possession or manipulation. This is indicated by her claim to know the unseen, as her jinn companion goes to the companions of the people of the house to find out what is happening, and then she informs them of it. Therefore, she should be advised and reminded that claiming knowledge of the unseen is a dangerous matter that could amount to disbelief, as Allah Almighty says: "And thus have We made for every prophet an enemy - devils from mankind and jinn, inspiring to one another decorative speech in delusion. But if your Lord had willed, they would not have done it, so leave them and that which they invent."