SPOILERS
I believe Gisette killing you in week 7 can result from "be tried as war criminals" or botching you blackmail attempt. I did the former and got an achievement from it. IDK about blackmail tho
What exactly are you doing that doesn't make Sarya trust you? I've always been nice to servants, help her with the drunk delegate, and got a perfect trial to raise her relationship enough. Without inviting her to stuff (though it was cool when I did for Onvu and girl's night)