If Cincinnatus Rex is warded and there are no creatures in the opponent's battleline, its Constant ability resolves, tries to destroy Cinncinnatus Rex, removes its Ward, then destroys Cinncinnatus Rex.
If Cincinnatus Rex destroys the last creature in the opponent's battleline in a fight, Cincinnatus Rex's constant ability will resolve and destroy Cincinnatus Rex before its Fight: ability can resolve.
If Cincinnatus Rex destroys the last creature in the opponent's battleline in a fight, Cincinnatus Rex's constant ability will resolve and destroy Cincinnatus Rex before its Fight: ability can resolve.