Alright, it seems he took the baldy's phone from chapter 1. Clever trick from the author. Also totally fit with the doctor "sleight of hand" skill that he showed earlier. That skill plus how people so shocked upon seeing the dead body, totally believable he able to pick it up without others noticing.
As for how he survived, it seems he use the his death card on the nurse, Nanase. Then since both of their phone can't be used to enter the shelter, he had the advantage because he can still use the baldy's phone to enter the shelter. The rules only said you can not give card to people who attacked by alien invasion. Since the baldy's death was by lasers from the starting room, the doctor can give life card to baldy's phone.