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Northern Patriarch is not killed by Valar Morghulis, does not need to be chosen for Valar Dohaeris to stay in play, is not discarded by The Doom of Valyria, can be saved while The Bloody Flux is revealed, and can have its STR increased or reduced while At the Palace of Sorrows is revealed. But all of that is only true if an opponent reveals those plots, not if you reveal them.
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If you reveal Varys's Riddle, the When Revealed ability you initiate with it is not considered to be an opponent's plot effect, so Northern Patriarch will not be protected from it. On the other hand, if an opponent reveals Varys’s Riddle and initiates the When Revealed ability on your revealed plot card, Northern Patriarch will be protected from it.
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Northern Patriarch is only immune to Omens while it is in play, so Ghosts of Harrenhal or The White Shadows can still put it into play from the dead pile.
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You can move power from your faction card, since that is a card you control in play.
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If the opponent moves power to cancel Northern Patriarch, the interrupt window for canceling the event is still open, so you can still play The Hand's Judgment or use Bran Stark (Core) to cancel the event.
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Max once per round (as opposed to "limit") counts towards all copies of Northern Patriarch, so you can only trigger this particular interrupt ability once, even if you have multiple copies of Northern Patriarch in play. (See Limits and Maxima. Note that a maximum does not usually appear on cards that remain in play through the resolution of their effect, but it works just the same.)