I was a bit confused by the photo session

I thought that was strange too, so I googled "death portrait". This was a real thing, common in the 1800s when photography was comparably expensive and reserved for special occasions. You can google it to read some articles and see real death portraits.

Photos of dead people seem to have been taken in other countries too like England (see The Others)

It was a custom in 19th century Europe and North America to do a portrait of a dead person. My museum has a portrait of a dead nun in its collection; the painter propped her up in a chair and did the painting quickly, I imagine, before she could start to decay. See also death masks--Beethoven's for example.

What makes this scene particularly painful for me is the fact that this is basically the only time Carmen feels her father's arms around her. And he's dead. God, I cried so much at that realization. But then, I cry easily at movies.