1. Say there is one character in the challenge and I reduce its strength to 0 with some non-terminal effect like forever burning. Is there a player action for him/her to naval a character in or does the challenge immediately end? What if I burn/kill it (I think here the FAQ says the challenge immediately ends)?

2. Say I have a duped noble in Martell. I ghaston bounce a greyjoy character, to which greyjoy then cancels with some cancel. Can I then do a save of the noble with the dupe on (the one i chose to go moribund:hand for ghaston), since we are still doing save and cancels step?ww

1. Say there is one character in the challenge and I reduce its strength to 0 with some non-terminal effect like forever burning. Is there a player action for him/her to naval a character in or does the challenge immediately end? What if I burn/kill it (I think here the FAQ says the challenge immediately ends)?

2. Say I have a duped noble in Martell. I ghaston bounce a greyjoy character, to which greyjoy then cancels with some cancel. Can I then do a save of the noble with the dupe on (the one i chose to go moribund:hand for ghaston), since we are still doing save and cancels step?ww

1. If you burn/kill it, the challenge will end before the opportunity for a player action that would bring in a new character. If you simply reduce its strength to 0, it stays in the challenge and the challenge resolves (although a side counting 0 strength cannot win a challenge, the challenge does continue).

2. The first portion of using GG is paying the cost. That means the character has to go from In play to Moribund: Hand as part of Step 1. (Initiation), not as part of step 3 (resolution). The save/cancel (step 2) step happens after initiation, at which point your noble is already moribund. In other words, you cannot save your noble with his dupe.

Said differently:

1. The challenge only ends if all participating characters are removed (from play or from the challenge). Lowering a character's STR to 0 doesn't remove it.

2. If your Martell character isn't moribund, you didn't pay the cost for GG. If you didn't pay the cost for GG, there is nothing for the GJ player to cancel. You can't "undo" a cost paid in Step 1 during the Step 2 save/cancel step.