if you fail to meet any terms of any deals you will destroy your rep and you will never get it back for the rest of the game. it doesn't even matter if it is your fault or not - you gets da blame.
if some Civ is wiped out and your resources were going through a road for that Civ you will lose your rep just as if you had purposely disconnected the resource.
Not quite. If the AI exports resources/luxuries to you, and you do NOT export any luxuries/resources to the AI, and you cut the trade route, the AI suffers the reputation hit. You do not suffer any reputation hit. I and others have basically documented this at length elsewhere.