If I use Impromptu Duel & my opponent has focused an Arrows Do Not Falter whose focus effect would kill my challenging personality before the duel ends, would the only surviving person be considered the winner of the duel and gain 2 honor?
arrows do not falter and Impromptu Duel
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
If I use Impromptu Duel & my opponent has focused an Arrows Do Not Falter whose focus effect would kill my challenging personality before the duel ends, would the only surviving person be considered the winner of the duel and gain 2 honor?
No.
Challenges and Duels: If a Personality involved in a challenge or duel leaves play during it, the challenge or duel ends immediately without resolution. In particular, Focus Effects that have not yet resolved at that point do not resolve at all.