One thing that's always bugged me and sorry if this has been answered elsewhere: wtf happened to Martok's bitch-slapped son from Way Of The Warrior? Unless I missed something, feels like he's never mentioned again, and fact that Worf was the one who dishonored him doesn't seem any impediment to him being accepted into M's house.
It probably should have been mentioned, I always assumed he died during battle sometime between Way of the Warrior and when the real Martok broke out of prison with Worf.
As for the morality of Kurn wanting to die, like they say in the episode judging it by human standards its murder, Worf even seemed to struggle with killing him because of this due to being brought up by humans.
Had Worf not either killed him or neuralised him Kurn would have found a way to die honorably or not (the consequences being whether you believe in the existence in an afterlife be it Klingon or other). Its a shame they didnt find a way to resolve the situation like they did with Kor.