Can any American successor state become a major power

USA. Or Superior.

Will the nau expand and if so to what countries

Could superioror establish a provisional Minnesota govt like Wisconsin

No American successor is going to really have reach outside of the continent. Major power in NA? Sure. Globally? No.

Most dangerous? Sicily being stupid.

NAU will likely grow to include much of western NA. Ass~, California, Victoria most likely ones for the next while.

Such a government already exists - International Falls.

Hmmmmmm. Now I may consider something, in regards to what I have read thus far......how long before the human species fully recovers to pre-Doomsday levels, then to the 2050 levels of our timeline and heads out to settle the rest of the Sol System, or even colonize other star systems beyond the Sol System? NOTE: This is a more speculative question, but I am mainly more concerned about Earth going back to pre-Doomsday levels of technology and full recovery of the human species.  

Oh. This is 100 years, not past that. *chuckles in an embarrased manner*. 

Not quite sure about population levels, perhaps that most likely only recover after technology has. Technology we are seeing anywhere between 15-30 years to get to OTL levels, so population could be said around 35-60 years (depending on which population figures you look at).

Nations will primarily focus on earth issues. I mean why look to send pointless satellites in space when you could be helping out survivor states and be gaining influence while doing so? Only essential communication satellites will be government's priorities, research satellites will not be sent for a while yet.

Hmmmmmmm. Well, I would assume human settlements in space are still past the 100 year mark, correct? 

Most likely I'm afraid.