-Dragonborn spoilers-
It is revealed in Dragonborn that the Empire pulled out of Morrowind and never came back after the oblivion crisis. The Dunmer haven't taken too kindly to their abandonment.
Hlaalu as a house was abolished for having so many imperial ties. Redoran has become the foremost house, and House Sadras has taken Hlaalu's spot in the council.
No, not from what we can gleam from the games and novels. It appears that they never formally declared independence. Instead, amidst catastrophe, the legions left and never returned; so the Dunmer continued on under their own terms. Great House Hlaalu, imperial collaborators, were outcast, and no longer sit at the Great House council. The agents of the Thalmor, who have free reign in the Empire, appear to have no such power in Morrowind. Power seems to be centered in Blacklight now, under the guardianship of House Redoran. Blacklight is said to be as grand as Mournhold/Almalexia was at its height.
Argonians appear to still raid as far as Solstheim, but they didn't occupy territory beyond the swamps of southern Morrowind: territory that they claim was originally theirs.