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Ferdinand apparently doesn't use the standard firesand but wind crystal pressurized cartridges to propel its bullets while the Peacemaker uses lightning crystals to increase its shot velocity and so it seems various magitek enhanced type firearms exist but the standard issue low tech firearms run on firesand which is a gunpowder analogue. Garlean's are also apparently the first to pioneer revolvers which allow multiple shots before reloading sometime before they became an Empire.
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As a Brd, I have purely magic arrows, and also normal arrows I pull out of nowhere and imbue with magic, and somehow shooting one "procs" the other. My accuracy with a bow has nothing to do with my eyesight or what glasses I wear, but what recycled clothing pellets I meld onto my shoes. I also can't shoot anything more than 30 yards away, just because. So good luck with seriously trying to apply logic in this game.