When units are destroyed by sword icons on house cards - how are the units chosen?
The loser choses. From the rules, page 21:

When a player suffers casualties, he decides which of his units are removed (unless stated otherwise by the text ability of a played House card). Remember that supporting units can never be taken as casualties in combat.
Note: Each casualty suffered destroys a single unit, regardless of Combat Strength. In other words, removing a Knight unit as a casualty still counts as only one casualty even though its Combat Strength is 2. For this reason, it is generally best to remove Footmen units as casualties, if able.