Can I trigger Robb's reaction when Robb himself dies?
No. The triggering condition for a reaction (in this case, Robb's death) is resolved completely, then reactions are triggered. So Robb will be killed and in the dead pile before you could trigger his reaction. You can't trigger the abilities on cards that are not in play unless they specifically say so. Since Robb doesn't say he can be triggered from the out of play, he can never be triggered for himself being killed or sacrificed.
Can I trigger Robb's reaction when a Stark character is saved from being killed (by a duplicate, Bodyguard, etc?)
No. If the character was saved, then it wasn't killed.