The Magic Power modifier determines how much you know about magic and what are the spells you have access to.
The Magic Potential/Affinity determines how much are you gifted in magic and makes your spells more likely to work and, in some cases, increases their effect. Having magic potential as a flag or as a trait is the same, the only difference is, if it's a trait, Witch Hunters can see it and treat you accordingly.
The lore you learn is the one your master taught you. If you learned from a fire wizard, you will learn the lore of fire. The only two exceptions are the High Magic and Dark Magic lores, available for elves, which can only be learned in their respective academies ( Hoeth and Ghrond). If an elven mage teaches an apprentice, he will get the lore of heavens (rather than high magic) or the lore of shadows (rather than Dark Magic).