After the fight resolves, if the creature that is being used to fight survives, all “Fight:” abilities the creature has, if it has any, resolve. A creature cannot fight if there is no enemy creature to attack. Therefore Fight abilities would not trigger.
If Horseman of Pestilence was to Fight, it would deal 5 damage to its target creature and sustain any damage returned from that creature. If Horseman of Pestilence was not destroyed his fight ability would trigger - Dealing 1 damage to each non-Horseman creature (this includes friendly and enemy creatures)
If a creature attacked Kelifi Dragon, and Kelifi Dragon survived the attack - Fight abilities would not trigger because Kelifi Dragon did not declare the Fight. However, Kelifi Dragon is considered to be fighting.