After looking at the trial of Vivec it seemed as if he was more powerful than Azura herself at that point, which brings up my question which may be dumb: does this mean he theoretically could remove the curse Azura placed on the Chimer?

I don't think he would want to even if he could. I guess he thought that the curse made his people actually even more special than before .

The other thought is more general: In most real world legends, lifting a curse usually requires a specific deed that has some relation to the curse, and even gods are bound to these requirements.

yes, but what's the point?