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The basic formula for physical damage appears to simply be: Attacker's AT - Defender's DF = Damage
Factors like land effect can significantly alter this equation, but I am unclear as to how. As a general rule, indoor damage will be far closer to this ideal equation then outdoor damage.
Different magic spells do a different amount of damage. Most bosses (particularly in the first half of the game) take about 50% damage from magic, while enemies weak/strong against a certain element take between 10% and 20% more/less damage respectively.
Flying characters can move anywhere with no movement penalty, Guntz and Adam can move anywhere non-flying characters can move with no movement penalty, and Zylo can move anywhere except for hills with no movement penalty. Other characters take between a 40% and 60% penalty to their movement rate on desert, hills, forest, and possibly a few other terrain types. Only flying characters can move over water, air, and mountains. (Shivers: Domingo is in a category all his own. For some reason, he can fly over water and air, but not mountains. Go figure.)