In English, "she shook her head" implies horizontal motion, i.e., non-verbally saying "no." Does the Norwegian equivalent have the same meaning?
Why do you need the på in this type of sentence? 'She shook on her head' has always seemed off to me.
If you omit the preposition, it sounds more like she's shaking the head of her decapitated enemy than her own, or perhaps even roasting it in the oven. Which, while sounding pretty badass, is probably not what you were going for.
Think of "å riste på hodet" as a phrasal verb.
Yes, that's what you would do when you greet someone.
If you were making an agreement you could say "De tok hverandre i hendene" although this could just mean that they were holding hands (context matters).