Yes, because the Nords and Dunmer have a long-standing "you go your way, we go ours" agreement. The Dunmer owe no fealty or taxes (though apparently some merchants do pay them)
You have no basis for that statement. There is no reason to believe the Dunmer don't pay the same taxes as the Nords. And why would they fight for the stormcloaks or the guards when they don't get regular partrols and the stormcloak use "Skyrim is for nords only" alost like a motto.
A leader is supposed to lead Ulfric doesn't do much of that for non-nords.
And can you think of no reason why a city that already has a large, restless Dunmer population wouldn't want to add Argonians to that mix? Like, maybe, the fact that the Dunmer enslaved Argonians for centuries and Black Marsh invaded Morrowind after the ancestors of these same Dunmer were fleeing the Vvardenfell disaster.
But the many of the Argonians in Skyrim were born there they don't appear to carry any hard feelings for the Dunmer whose ancestors enslaved their cousins up until around the time of the Oblivion Crisis. (Slavery was ended in Morrowind not long before the start of the 4th Era). The Argonians are forced to live outside Windhelm because they are Argonian.
Theres argonians in riften city
Riften is controlled by the Empire so naturally it have less issues then a stormcloak city.