Is the killing of one of two disputing parties considered Qadaa’ and Qadar (Divine Decree and Predestination), and what is the ruling concerning the disputing parties on the Day of Judgment?

Everything that occurs in the universe happens by Allah's decree and destiny. Allah's pre-ordaining of such events does not mean that a person is coerced into their actions, for Allah has granted the rational human being will and ability. If a quarrel leads to killing through a deliberate act, the killer is held accountable in this world and the Hereafter, and their invoking of destiny will not benefit them. If the fighting is due to tribalism or partisanship (asabiyyah), then both the killer and the killed will be in Hellfire, provided the killed person was eager to kill their opponent.