As to #1, I take the North as being vast as spread out. For whatever reason, I assumed that they all spread out after the big battle and went back home. Maybe it's just because of the similar names, I took the Karstarks as being close geographically to Winterfell, and maybe more likely just to side with whoever is there. Rob didn't help matters by beheading Daddy Karstark either. They are on board with team Bolton. I fully expect houses closer to the Wall (maybe that includes the Umbers) to fall in line with Jon as he marches south to whoop the #### out of Ramsey. Also, one of the houses has to be hiding Rickon, so there have to be people that know a Stark is still alive and are still loyal to that family.