Balgruff, and all the other Jarls and stewards loyal to the empire, are safe and sound. They are merely stripped of their Jarlhood. They live in the basemant of the castle of Solitude.

You "conquer" Skyrim by doing quests in all the major areas. These quests are more about killing Imperials than harming other Nords. The story is pretty white-washed and convenient that way.

The stormcloaks do not fall apart. They conquer Solitude and accept the surrender of the Jarl Elsif. General Tullius and Legate Rikke are killed by Ulfric, Galmar, and the player. Thus ends the foothold of the Imperium in Skyrim. There's a dialog between Tulius and Ulfric which, imho, finally justified my siding with the Stormcloaks.

In the aftermath Ulfric refuses the mantle of high king until a Moot can be formed (though it would be a mere formality). Ulfric and Galmar talk about focusing efforts on rebuilding Skyrim and fortifying it against further Imperial meddling or Thalmor invasion. Galmar is trusted with ensuring the Jarls work towards this end. The player is left with standing orders to hunt down remaining Imperials, but otherwise his service has ended and with great thanks from Ulfric.

Also, Ulfric allows Elisif to remain the Jarl of Solitude, which made me happy since I like her.