The brown streaks on the hive are a sign of dysentery, not necessarily of
Nosema.  Bees can have dysentery without Nosema and vice versa.  However,
dysentery is a very efficient way of spreading nosema if it is present.

You could make a microscope slide of the faecal matter from the streaks and
examine for Nosema before treating.  It is usually not a good idea to treat
for an ailment that is not present.

Dysentery is usually associated with stress and you have described how the
colony has been stressed.  I think you are not far wrong in your suggested
remedy.  Reduce the volume of the hive; secure from predators and feed.  What
you feed is governed by strength of the colony and the climate where you are.
 As you are relatively inexperienced ask a local beekeeper what he would feed
at this time of year.
Good luck
Chris Slade