At the end, Elizabeth is dead. But when Adam carries her, her arm is completely wrapped around his neck as he carries her to the fire. A dead person's arm could not maintain such a position, even if placed there by the carrier; only a live person, using muscles, would be able to keep the arm up like that. Without muscles, it would just hang down behind him. Also, as he carries her, his left arm is supporting her torso and her head is upright. Again, a head maintaining such a position would be impossible for a dead person. A dead person would have no muscles to keep a head up. Instead, it would droop backwards in the direction of gravity. Finally, as he places her down on the burning logs, her head slowly descends, whereas it should fall down, since, again, there are no working muscles to control its descent. All of this is also true if she were merely unconscious.
At the time of this film, it is unlikely that any cellular phone would have sufficient power to be used for navigation during a walk of twenty miles (even at superhuman speeds).
While being true to the spirit of the 1818 story, it seems unlikely that a scientist today was not actively looking for their escaped creation. At the very least, they potentially had legal liability for a deadly creature on the loose.