Cassandra was seeker and part of her job was dealing with mages and magical threats pretty much sure she does know about magic and its threats a lot as templars do.
Also pretty much Viviene is corrupted and power hungry ,not to mention she is on other side of barricade as mage i wouldn't trust her with keeping check on mages as i wouldn't trust shady prisoners with running the prison.
Right, but I'm not referring to combating magic. I'm talking about researching it. Cass doesn't know anything about that, but Vivienne does. Also, Cass should rebuild the Seekers. She can't rightly do that as Divine, since the Seekers are a separate order from the Chantry.
Her involvement in the Game is Celene's doing. Vivienne was First Enchanter, and then Celene requested her council at court. Vivienne then turned the position of "court jester" into one of respect. Surviving the Game doesn't necessarily make you corrupt. My male human mage beat the Game without being corrupt. If anything he exposed corruption... and... danced like a man... not a ballerina.
As for killing that guy, she only does that if the Herald demands it. So does that make the Herald corrupt? Now, I will agree that the law is nothing to go by when deciding morality. Orlais permits all kinds of immoral stuff after all. So lets look at this from a moral perspective. Did the punishment fit the crime? Well, the guy attempted to draw a weapon on an unarmed person (if a mage). It can be reasoned that he intended to kill the Herald quickly. So, attempted murder. I'd say that's pretty worthy, even if it had failed spectacularly, which it would have. So I don't see killing him as corrupt. If left to Vivienne, she will just humiliate him and send him on his way to try and regain some honor by fighting in the war.
As for her station. She rose in the Circle because she was talented, knowledgeable, and compliant with the rules. It's like she'll tell The Iron Bull, some pound on the wall mindlessly, others use the tools at their disposal. Vivienne used her toolset to get over, under, or around the wall. So it's only natural that she would see herself as better than the mages who remain stuck in their ignorance. She sees individuals of different levels of worth. That's all.