Does the numbness after surgery improve? At what point can you assume any numbness is going to be permanent?  

Yes. For upto six months but if it's in areas other than around the incision u ought to discuss it with your doc much sooner.
6 monts to a year. Without more detail i cannot be sure as i don't know what type of surgery was done, but if you mean numbness around the scar, that recovers slowly over 6 months to a year. Anything after that is probably permanent. If there is a large area of numbess on the far side (distal side) of the incision, it could sometimes need further treatment if the area of numbness is large or debilitating.