do you trigger when you win a challenge effects before or after the end of the challenge?

Triggering responses is considered part of the challenge resolution - and therefore technically take place before the end of the challenge. Otherwise, cards that said things like "Response: after you lose a challenge, kneel a character to choose and kill a participating character" would be useless (since, after the challenge is over, there are no "participating" characters).

johnn0411 said:

To trigger any such effect, the winner of the challenge must have been determined and it must be you, which usually happens near the end of the challenge.

After defenders have been declared and no player wishes to take an action, the

1. determine winner of challenge (i. e. compare STR of participating characters),
2. implement challenge result (i. e. satisfy claim),
3. award rewards for unopposed challenges (i. e. claim one power) and
4. award renown

steps are executed.

The earliest opportunity to trigger a save/cancel response would be during the determine winner of challenge step ( Example card: True Power ).

Then, after all steps above are complete, any passive effects automatically trigger. This includes the “Deadly”, “Vengeful” and “Vigilant” keywords ( Example card: Daenerys Targaryen ).

Then, any non-cancelling response effects may be triggered; this is probably the most common way of triggering a “after you win a challenge” effect and there are many cards with such an effect. This, however, is the only opportunity to play them ( Example card: Support of the Kingdom ).

After that, the challenge ends and Moribound cards leave play. Any other effect (such as an “Any Phase:” or “Challenges:” effect) can be triggered after that, when players can take regular actions again ( Example card: Wedding Feast ).

ok and when do, until the end of a challenge effects stop applying?

As soon as moribund cards leave play.

and if the card is not leaving play?

The challenge ends when the framework action window for resolving the challenge closes - which happens after passives and Responses to winning/losing the challenge, settling claim, claiming unopposed power, and/or claiming Renown power have all been played and resolved.

You physically remove moribund cards from the table at the end of every action window.