A thoroughly sensible move, in my opinion.
Might be, these are more traditionalist Dunmer than in Riften so there could be the threat of violence between the groups. Yet we only see one Dunmer exhibiting racism towards the Argonians to my knowledge and not much about the Dunmer in the Grey Quarter from the Argonians which I find weird. Might be just another Bethesda oversight, but if there was animosity between Argonians and Dunmer you'd think it'd be shown by more than just one Dunmer.
The Stormcloaks don't do anything about a string of murders of high-ranking Nord women, either, or the capture of Fort Amol. Their lack of protection from bandit raids is more to do with the war, or Jorleif's ineptitude, than it is with deliberate policy.
Could be, not sure why nothing has been done about some of these issues before the civil war began though. The Dunmer and Argonians have been in Windhelm a long time now.
She is questioned about her connections by Captain Lonely-Gale, and nothing happens to him.
I haven't seen this conversation myself but he's not harassing her besides questioning her associations is he? He'd probably be okay as long as he didn't pursue it or screw with her somehow. Or maybe he'll soon be sleeping with the Slaughterfishes for asking too many questions

And if they crossed Nurelion? What shady organization is he using? He can barely fight as it is. You brought up that it's likely because he's a famous alchemist. That's exactly it. He provides a service to the city. People that provide a service to the city tend to be looked upon better.
Yep, his utility helps him out. It's like if there's just one doctor in a town you don't mess with him because you'll be screwed if something happens and you need his help.