1) Sevario was an unfortunate casualty of war. Those tend to happen in war. The Imperials tried to cut your head off simply for being at the wrong place at the wrong time.
2) Stormcloaks don't buy from Arcadia since they fear that she could poison the potions. Considering that before the battle she shows obvious disdain for the Stormcloaks, it is no surprise that they don't buy from someone that hates their group. Would you buy something from a person that hates your faction?
3) Adrianne can be explained by her being the former steward's daughter. Stormcloaks could potentially see her being angry over her father being exiled so they could fear her giving them faulty weaponry. In addition, why would you get weapons from a blacksmith with ties to the previous regime when you can get weapons from a smith who is both known as the best smith in the entire country and is a known supporter of your faction. It isn't based on race since if it were, the BOSMER and BRETON in the city would complain about Stormcloaks not buying from them. Furthermore, an Imperial owns a house in the rich district of Windhelm and the Stormcloaks in Windhelm advise you to go to the DUNMER merchant in Windhelm.
4) Heimskr doesn't seem too bothered about that. Also, read part 1. It's war, things get damaged during a war. The Imperials also use catapults during the siege of Windhelm and those no doubt damaged parts of the city.
5) Hulda also says the following line afterwards "In other words, nothing's changed." That means everything is still the same with regards to the bar.
6) The guards also hit on Carlotta when the city is controlled by the Imperials. Nothing ever comes of it
7) Sinmir is supposed to leave the bar yet he doesn't due to a bug in his pathing.
8) The Imperials also don't do anything about it.
9) The Battle-borns are practically snobs. The only good ones are Jon, Lars, and the one on the farm. You really thing the Battle-borns wouldn't do the same if they were in charge of the city?