Would I have any rubbing issues with 16x8 +45 all around? Would it be ok to run staggered tires on this square setup? What sizes would you recommend (width and sidewall)

 

Why do you want to run 16x8 square in the first place? It's too narrow for the rear and 16's don't have the tire choices that 17's do. I wouldn't run staggered tires on non staggered wheels, it is counter intuitive.