Bjorn is going out to become a man. He will make his way back later.
Sure he has been in many battles at this point but he wants to go out and prove to his father that he is a man and can make it on his own if need be.
Legetha is a woman who was not going to stay in a relationship with Ragnar after he came back with another woman with his child in her. Ragnar has moved on, Legetha has moved on.
Rollo has to be his own man and in real life he becomes a ruler
Ragnar spared Floki because he found out Floki's daughter died and Floki's wife is still there for him but at the end Athelstan's ghost visited him and said mercy mercy mercy...he took that to mean mercy for Floki.
The daughter in law is not a woman to be trusted...she had relations with Athelstan and now her father in law by her own will.
The Son knows his wife is not a good woman. I imagine he figures if she can stray, so can he.