I would like to colate a few things which didn't seem clear initially because of subtle wording, but can still be clarified using the the rulebook and close examination.
1: "Playing" a card is the same as "Marshalling", ie. Not challenging or kneeling etc, but when you initially put down the card.
2: A "House Lannister card" or "House Stark card" litterally means any card with the wolf or lion emblem in the corner and not one of the grey unafiliated cards, it does not have to be someone from the direct house/family in name.
Example: Tywin Lannister, Lannister Guards, and The Hound are ALL House Lannister characters. Shae and Littlefinger are not.
3: Lannister Guards, if the plot makes you discard cards in your hand " when the plot is revealed", then the Lannister Guards allow you to draw a card " after " you have finished discarding. Equally if the plot kills the guards " when" the plot iis revealed then they aren't around for " after".
4: The Direwolf is not a character and cannot be kneeled as a character by any of the Lannister cards. Yes this mean the Lannisters will almost never be able to kill anyone in a military engagement, because the defender can choose whoever has the direwolf and then just kneel the direwolf instead.
5: Shae. The Challenges section text on her card is an "action" and therefore can be played during the opponent's challenges turn ie. Before the opponent makes a challenge, even as first/active player with initiative .
Technically the first/active player can always play an event (not a challenge,) first, but the Starks have no event cards that can do anything to Shae, so it doen't really apply here.
Example the other way round: Lannisters have initiative/active/first player, Starks have "Septa Mordane" marshalled and would like to kneel her before the Lannisters attack. She CAN do this BUT the Lannisters could play "The Lion's Cunning" if they have it, to pre-kneel "Septa Mordane" because they have initiative/active/first player.