The rest of the world just dies slower.
Not necessarily. Depends on the winds, atmosphere, large weather storms, time of year and if it’s a full scale eruption. But you can probably count on folks 500 or more miles north of the detonation into Canada, the Midwest and much of the northwest not surviving. Get ready for world wide cooler winters with supplies of everything being scarce.
I don’t think it would be a species killer, but a whole lot of people wouldn’t make it.