So I just started playing FF3 again (via a rom) and this time I have two mages in my party, a red mage and a white mage, along with a fighter and a blackbelt (I'm on the part right before Jinn but I'm leveling up).

When I equipped the Ice spell on my Red Mage it said I was allowed to cast it seven times. But that doesn't seem like nearly enough if I were to reach the end of the game with the party I have now. And none of the FAQs I've seen have explained the magic system in detail (I even checked the front page and found nothing on MP). So my questions are:

1. Does the amount of times you can cast a particular spell go up?
2. If so, then how does it happen? Is it via level up, skill points, or something else?