It’s early i had that question yesterday
Answer and explanation:
Proctor stops himself then changes his mind about not confessing because he wishes to save his life in order for him to enjoy life with his family and wants to see his kids growing up. In addition to this, he wants his kids to grow up at least with one living parent at their side since his wife had been exectued under Death Penalty before.
No, this would not be necessary - what would happen is regulated by the presidential line of succession: the Speaker of the House, and if illegible (e.g. not born in the US) the President pro Tempore of the Senate would become the next president.