The word hen was introduced as a replacement of the gender-specific hon ("she") and han ("he"). It can be used when the gender of a person is not known or when it is not desirable to specify them as either a "she" or "he".
One can say: her and him?
I expect there will be different words for "her" and "him", not the same as "she" and "he". No doubt they're coming up!
No, it would be 'henne och honom'.