I could see abilities being learned in job quests, though considering the pattern with new jobs BLU would probably start with at least half of its spells already at level 50+.

I doubt they're going to introduce any traditional blue magic system where you go out and learn spells though, and I doubt they're going to add a spell glamour system to have multiple versions of functionally the same song. Maybe time will prove me wrong, but while the job may have a unique mechanic or two in its gameplay with all jobs having a gauge, I wouldn't count on going out into the world to learn abilties or having anything unique about how the job functions beyond the usual job mechanics.