Siege of Winterfell/Claiming Power AND Frozen Outpost

By BenStark, in 2. AGoT Rules Discussion

1.) Siege of Winterfell states that you cannot claim power for house except during a Military challenge.

Does this include winning Dominance? I.E. If I'm playing Siege of Winterfell and I win Dominance, do I not claim power during the Dominance phase?

2.) Frozen Out post states "Challenges: Kneel Frozen Outpost to choose and stand 1 defending character. Until the end of the challenge, that character gets +2 STR (+4 STR instead if it is a [war crest] character)."

How does this card resolve? I believe it resolves the following way: I declare a Defender. I then kneel Frozen Outpost to stand said character (which continues to participate in the challenge) and give it +X strength, and then resolve the challenge. Am I correct in this assumption?

BenStark said:

1.) Siege of Winterfell states that you cannot claim power for house except during a Military challenge.

Does this include winning Dominance? I.E. If I'm playing Siege of Winterfell and I win Dominance, do I not claim power during the Dominance phase?

BenStark said:

2.) Frozen Out post states "Challenges: Kneel Frozen Outpost to choose and stand 1 defending character. Until the end of the challenge, that character gets +2 STR (+4 STR instead if it is a [war crest] character)."

How does this card resolve? I believe it resolves the following way: I declare a Defender. I then kneel Frozen Outpost to stand said character (which continues to participate in the challenge) and give it +X strength, and then resolve the challenge. Am I correct in this assumption?