Can a Scurvy Cutthroat discard an attachment when it's attaching to someone while it's coming out of the shadows? Most immediate example for me'd be Venomous Blade.

No, because bringing a card out of Shadows is not the same as playing a card.

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Follow-up question then: Can the cutthroat discard stuff attaching to his controller's characters (i.e. Fishing Net, Milk of the Poppy)?

Sure he can...any reason to think otherwise? (unless of course your opponent puts that Milk of the Poppy on him. In that case he doesn't have his ability any more : ) ).

schrecklich said:

Similarly: If KotS Theon were to kneel a location that has to kneel to perform its action (i.e. Alchemist's Guild Hall), would that prevent it from using its ability?

I'm unsure here since my previous CCG experience includes stuff like Magic and VS, where declared actions resolve in reverse order of their declaration (i.e. a Counterspell works because it was declared after the spell it's countering, and thus resolves before it).

Kneeling a location would prevent it from using its kneel ability. In this case, effects are always resolved completely once declared with a few exceptions. The main exceptions are that Save/Cancel responses can interrupt the resolution of an effect and modify it and cards that are removed from play become "moribund" (meaning that they are both in play and out of play for the purpose of triggering any last responses to the effect that caused them to leave play before they are totally removed from play and thus can't trigger their effects any more).

You might want to take a look at the FAQ on the support page for AGoT LCG. It has a lot of details about the timing structure of the game in it. If you have been playing Magic long enough, I'd describe the rules for AGoT as being similar to the pre-6th Edition rules for Magic back when "Interrupt" and "Mana Source" were still card types.

Hamster Friend said:

That kind of feeds into the other question: in this game, every initiated effect is completely resolved before the next one ever gets a chance to initiate. There are no "stacks" or "chains" of effects in this game. The only exception, as already mentioned, are "save" and "cancel" Responses, which are the only things defined in the rules as able to interrupt the initiation and resolution of an effect.

So, if effect #1 kneels a card that has a "kneel to..." effect of its own, that "kneel to..." effect cannot be activated after effect #1 initiates, but before it resolves. (Unless the "kneel to..." effect is a Response that would specifically saves or cancels against effect #1 - a very rare occurrence.) You either have to anticipate effect #1, or give up the ability to pay the "kneel to..." cost until the card stands again.