Sometimes task update requires some time. However, it will be added to your count anyway. Try to re-enter the game and check if task's status was updated. Also check if you have fulfilled all the conditions of the task (for example, "within one battle" or "in one shot").
Selection of rivals is engaged by a special program - the balancer, it chooses your opponents considering many game parameters. One of them is your highest mercenary in the set. Depending on your experience of playing on it (amount of battles, amount of kills) the enemies are chosen. The longer you play, the stronger enemies become.