So we were playing a four-player melee. Our Baratheon friend has Brienne of Tarth in play. Her character text says:

"While Brienne of Tarth is participating in a challenge, opponents cannot trigger effects"

What counts as an effect? Events only? Character responses? What about passive abilities in their text?

Taken straight from the faq

(3.6) Triggered Effects
Any effect that a player chooses to execute is
considered a "triggered effect." Thus any effect
that begins with a "Phase:" or "Response:"
is a triggered effect. Also note that playing
an event card is thus considered a triggered
effect. A "triggered ability" is a triggered effect
printed on a card already in play

Thanks a bunch! Where is this FAQ thing?

On the support page , specifically the FAQ is HERE.

I have another question.

House Dayne Skirmisher:
"Any Phase: Kill house Dayne Skirmisher (cannot be saved) to draw 1 card. Then, each opponent chooses and discards 1 card from their hand.

Can I use HDS to satisfy a military claim, then trigger his effect? Or can you only use these effects independently?
For example: Person A attacks me with a military challenge with a claim of one, and he wins. I choose to satisfy that claim by killing HDS, and I want to trigger his effect. Is this legal?

digidestined36 said:

First, once you kill a character, you cannot kill it again. The Skirmisher can either die for claim or die for his ability, but not both. It's no different from not being allowed to kill your Skirmisher 3 times to draw 3 cards because he can only die once.

Second, the timing doesn't work. Once you start resolving the challenge, you have to finish the process before triggering any new "Any Phase" or other actions. By the time you are done resolving the challenge, anything killed for claim is going to be in your dead pile.