Not rly as i said who was that did that they were mages. 
So, yeah, proving the point. Saying that because mages have done something, any or all mages will do something, is a fallacy.
No she wasn't unless you mean that after she killed son of viscount and hawke informed her about that.
Nope. Hawke doesn't stop Patrice once during the story, while the Grand Cleric clearly knew the qunari were there.
It isn't necessary to aid him of course not do anything about him is stupid unless you don't care hawke rly didn't caused that only anders.
Hawke knew Anders was an abomination and allowed him to roam free, but constantly went after the smallest of treats in the city. Yeah, Hawke let Anders do what he did, and it's Hawke's fault that thing went out of control.
You can inform her if you refuse anders help him in chantry otherwise you don't know what he is up to so you can't warn her.
You don't need to know what he's up to, to tell the Grand Cleric to watch the rogue mage that's in the Chantry, clearly identified by dressing like he's from Tevinter.