What is the ruling on publishing pictures of the deceased, especially those who passed away a long time ago, with the aim of invoking mercy upon them and praying for them? Is it permissible to praise them unjustly, and what are the limits and precautions for this action?

There is no harm in announcing a person's death and requesting prayers for mercy upon them, nor in mentioning some of their good and sincere deeds. This falls under testifying to the goodness of a benevolent person and encourages the living to do good. However, it is not permissible to state definitively that someone is a martyr; rather, one should say, "It is hoped that he is a martyr." What is prohibited in this context is mentioning virtues for boasting, lying, or inciting sorrow, grief, and wailing, or stirring up emotions about someone whose death occurred long ago.

As for placing their digital image on the internet, there is no harm in it as long as it is not printed on a physical medium.