Rules ref states the redirected challenge is "considered to have been initiated against the original opponent, but it resolves against new opponent" - this means that the new opponent cannot trigger "when a challenge is initiated against you" triggers (but the original target can) e.g. Core Eddard Stark stand reaction.

Should this be “printed cost X or lower cannot be declared” or is it this specific cost can’t be declared?

Only effects specific cost X characters, see Stannis's Cavalry for a similar wording. —

Does the new "Shadow (X)" overwrite the original shadow cost of a card already having shadow, or do they keep the original shadow cost, or have two shadow keywords?

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It gains an additional instance of the Shadow keyword. Per the rules for Shadows: "If a card has multiple instances of the shadow keyword, each with a different (X) value, the player controlling the card may choose which instance of the shadow keyword is used to bring the card out of shadows." —

Does this work with Walder Frey?

The Lord of the Crossing agenda?

Making a Frey deck, cause I like to play the anti hero

Cheers

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When you make your third challenge with Lord of the Crossing, you can stand a participating character whose strength was raised. —
Whoops, hit enter by accident! If you attack in the third challenge with a Frey character, Walder Frey will also join the challenge and have his strength increased, and so you can stand him. —

Rules FAQ

  • King’s Landing does NOT permit a player to marshal a location into shadows. King’s Landing allows you to “marshal a location” from your discard pile, and marshaling a card into shadows is not considered to be “marshaling a location.”