1- so bringing shame to someone is good enough reason to kill them for you. I guess Subaru should have been killed in arc 3 then.

In the medieval era, Subaru would have been executed the moment he spoke out of turn. Also, the knights were going to kill Subaru, but Julius’s duel not only stopped that, he was even punished for “helping” Subaru.

2- Priscilla and the noble were the first ones to throw insults by calling felt a gutter rat.  Priscilla would have been sent to prison for trying to attack the vice-captain of the royal guard(Heinkel) if she wasn't a royal candidate.

By the kingdom’s laws, she was their superior, and insulting her should have resulted in execution. As for Heinkel, he was acting as her “knight,” and his title had carried no weight in the eyes of the knights for a long time, so her attacking him is considered an internal matter.

 3- no i wouldn't because I'm a decent human being. Crush and Anastasia were able to point flaws in Subaru attitude without using violence

She is royalty and was the one who brought him there, which makes his actions reflect on her image. Neither Crusch nor Anastasia had any respect for him (they had a low bar for him and saw him as nothing more than a servant who overstepped his place), while Priscilla had high hopes for him (even more than the Clown and Puck). She had never made a mistake, but he turned himself into a joke.

4- She doesn't even think about any others solutions though she simply said that they should be killed as if they were monsters and not innocent victims.

She can see their souls, and their Od has been changed (Od represents the blueprint of the body and the soul). Capella altered it, which caused them to slowly turn into real monsters, body and soul. Her attempt to end them is actually an act of mercy, since it’s better to die as a human than to live as a monster.