Мафия 59. Mystery of the haunted house

I didn't understand how to interpret this.

Added 30 seconds later
So, she possesses her brother's body, right?

Apparently, yes.

Also, there are doubts about possessing the player, specifically when killing/executing the mafia boss while he's in the player's body. It was implied that you first need to execute the victim (if Fabien is dead and can't free the body), and then deal with the ghost. But I'm not sure.

The question here is how it's displayed. If it's more or less clear and you can identify the player who was possessed, then when the victim dies, there's no point in touching the ghost; just indicate during the execution that he has left the victim's body. The same applies to the ranged attacker; just give the instruction that the ghost has left the victim.
If the indication of possession is vague, then it makes sense to reveal the ghost's nickname when the victim is executed. That is, they executed Petya, and Vasya flew out of his body. Or, if Petya was killed by the ranged attacker, then the ranged attacker reveals the nickname.
If the boss has possessed someone's body, but they are going to execute him specifically, then it makes sense to indicate that the execution did not take place due to the absence of the person to be executed.