Does this QHORIN Halfhand character kill two characters after winning a military challenge? One for claim, and another from the Reaction text?

Qhorin Kills just 1 character, for his effect. The kill for the mil claim is not "done" by Qhorin. —
This said, You kill 2 characters, 1 for Qhorin effect and 1 for mil challenge —

Advice: If you are the first player and marshal this card on your turn, it gives your opponent the 1 extra gold when he gains gold for plot. Try to avoid this.

Rules FAQ

Triggered abilities are preceeded by bold bold (i.e. Action, Interrupt, Reaction).

Forced abilities are not triggered by players and are unaffected by this plot.

This plot does not affect events, plots, or agendas.

Rules FAQ

This reaction takes place during framework step 2.1, before either player draws their cards.

Rules FAQ

If an opponent plays Nightmares on Warrior’s Sons during a challenge, they will not be able to trigger their reaction.

If an opponent plays Treachery to cancel Warrior’s Sons reaction, they can then react to Treachery.