Is it permissible for a widow observing her iddah to leave her home for a photoshoot, or for a photographer to enter upon her, in order to complete the procedures for a death grant?

If a woman observing iddah (waiting period) after her husband's death needs to go out to have her picture taken, there is no harm in that. There is also no harm in the photographer entering her home to take the picture, provided one of her mahrams (unmarriageable kin) is present, and on condition that she spends the night in her home.