If anyone knows/can figure out what the different symbols mean on the Ability screens, that would be great.
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Figured out that the one at the top by 'Quick Reflexes' is for passive skills that you don't have to equip. They're often linked to additional Square-combo moves you can do, as well. Haven't figured out any consistencies between the other arrow symbols just yet, after about 5 hours.

One thing I did learn is what the abbreviations next to the Spell names are, like the BOM after Blizzard.
BOM = Bomb
RF = Rifle
SHG = Shotgun.

It's shorthand for how the magic is 'launched' from you. Each individual spell will say how the magic bullet behaves, but if you can't see that description the shorthand helps.