I've been playing the game for a few years now, and I just realized something : if a character that is committed to the quest gets damaged during the staging phase and gets kill, do you still count its willpower after it dies?

You won't count its will. The reason is in the third step of quest you count up the will of characters committed to the quest against the threat of the enemies. If the character is killed then it isn't committed to the quest any more. This is true in combat too, if a defending character is killed as a result of a shadow, before you compare defense against attack, then the attack must be considered undefended!