Suppose that under a revealed Valar Morghulis plot, both players have two characters on the table. The Greyjoy players has 2x The Iron Cliffs, each with 2 gold on them.

The Greyjoy players deducts 1 gold from each Cliff to save their characters. Next, the opponent responds and "kills" their own two characters via Harrenhal to cancel these two saves.

My main question is, can the Greyjoy player now deduct the second gold from each Cliffs card to save the characters? Or is only one save attempt (which has now been cancelled) allowed?

Further (secondary question, an aside on Harrenhal), can the Harrenhal player now re-use one of the same characters they had already "killed", thereby cancelling a third save and resulting in the Harrenhal card being immediately removed (as per its errata as I understand it)?

On the main question, my suspicion is that the Harrenhal response occurs within the saves/cancels segement and that any number of other save attempts can be made to save from the original Valar. More broadly, that if a given save attempt on a particular character is cancelled, then further save attempts may be made on that character.

If this is the case, then The Iron Cliffs would become so much more important than The Iron Mines now that Harrenhal is there.

On the (secondary) Harrenhal question, I'm really not sure. I would like to think that the same characters cannot be used, but would like to understand why that it so as per the timing frameworks. During the Valar event it seems the characters are moribund and thus can be used to pay the Harrenhal cost; why would that not also be the case after they had been used to pay the Harrenhal cost earlier in the window, meaning that a single character could be used repeatedly to pay the Harrenhal cost?

The relevant rule here is "a response can only be attempted once for each trigger". The Cliffs' trigger is a when a Greyjoy character would be killed, so there are 2 triggers, one for each Greyjoy character. The Cliffs are separate cards, so their responses are separate (but each Cliffs has only 1 response). Let's say you used Cliffs1 to try to save Char1 and Cliffs2 to try to save Char2. It isn't legal to use Cliffs1 again to save Char1 and Cliffs2 to save Char2, but it is legal to use Cliffs1 to try to save Char2 and Cliffs2 to try to save Char1.

Now, about Harrenhal. Cancels of an effect indeed happen before resolution of that effect, so no characters are moribund for Valar's effect when cancelling saves for Valar. However, paying the cost for an effect happens during initiation of that effect, so a character killed to pay for Harrenhal's response becomes moribund immediately (even before cancels and saves for Harrenhal's response) until the end of the action window (in which Valar Morghulis was revealed) and is therefore not available to be killed another time.

Thanks a lot pal, all clear!

You're welcome.