Big Problem

As soon as he saves Emma, he should disappear because then he would never have built the time machine to begin with. This movie assumes that the time machine then never existed moments before her death. So Emma dies and he must try again in an infinite loop or until he decides not to go back.
Emma dying all these different ways makes no sense. It's as if fate is causing her to die. If he saves Emma to begin with and them she dies a few minutes later then he travels back in time a few minutes later. But by that time Emma already died initially. If he saves her initially he does change the paat and she dies minutes later. But then he goes back later... He should disappear when he saves her.
He should have just taken her before she dies and brought her to the future. Since he can change the past (causing Emma to die at a later point) she should exist. But the movie also assumes that if she doesn't die then he never makes the machine. It is not consistent.