If the Archfiend targeted by “Battle-Scarred” is flipped face-down, then the effect of “Battle-Scarred” disappears and “Battle-Scarred” remains on the field meaninglessly.
You can select an Archfiend that doesn’t require you to pay Life Points as a target for “Battle-Scarred” (such as “Summoned Skull”, “Archfiend Soldier”, or “Fiend Skull Dragon”).
When your opponent takes control of your Archfiend targeted by “Battle-Scarred”, then your opponent must pay the cost for the Archfiend, and then pay the cost again because of “Battle-Scarred”.
When an Archfiend is equipped with “Heart of Clear Water”, it is not destroyed if it was targeted by “Battle-Scarred” and “Battle-Scarred” is removed from the field.
If your opponent doesn’t have enough Life Points to pay for “Battle-Scarred”, nothing happens to your opponent, you must still pay for the cost of your Archfiend, and “Battle-Scarred” remains on the field.
If “Battle-Scarred” and “Pandemonium” are both active, neither player has to pay for Archfiend costs or for “Battle-Scarred”