This is more a test of your new-found devotion to the side of good than it is a fight.
You've just got to skip a few turns by defending or using "Cover," and you'll eventually "win" by not fighting.
If you've attacked already, that's okay, but the fight won't end until you've chosen not to continue your aggressive behavior.
In general, most weapons that aren't metal will explicitly say so in their name. For instance, Cid can freely use the Wooden Hammer, but his other mallets won't be usable. The same is true of the Ancient Sword for Cecil, though if you've sold or missed that, he'll need to use a Bow, Staff, or one of the elemental 'Shard' weapons available in Troia. Additionally, Yangs claws are all considered non-metal, as are all Bows/Arrows, Rods, and Staves that don't explicitly claim to be metal. (Mythril is considered metal).
Shields are all considered Metal, as are Iron and Silver rings. (Use Ruby Rings).
For Armor, there are light/leather options available in the nearest town, but in general, the names should clue you in; the Kenpo Gi, Feathered Hat, Headband, Gaia Gear, Bard's Tunic, etc. are all solid options.
Additionally, all Metallic equipment is flagged on the Wiki here, if you need to double check. (Armor here.)
Best Answer
In the original incarnations, Pray was 50% chance to cast Cure, and a 50% chance to do nothing at all. The fact that it was just a cast of Cure made it somewhat less appealing later in the game when HP is higher and more powerful healing is possible.
In the DS/mobile versions (which you are playing):
Beyond the chance to fail, Pray is otherwise unlimited and no ill effects will occur from its (over)use. Abuse away.