Hi Benny,
Thank you for your questions.
#1: You are right.
#2: If the game object has no collider attached, no collision event can be triggered by this game object.
#3: The Rigidbody on a parent game object acts as a compound collider. It collects the collision information from the colliders on the child game objects. If you attach a material to the rigidbody, the colliders on the children get this material attached unless they have their own material.
Did this clear it up for you? 
See also:
- Forum User Guides : How to mark a topic as solved