Ok, two XP spent to gain a dot of academics. However, Blaze also gains a beat towards his aspiration of purifying the locus leaving him with 0 beats and 3xp. Updated on your character box.

You are correct regarding 1 roll a day, so yes you can work on it daily. I count two more successes, leaving Blaze with 4/10 successes. Let me know if you want to spend a WP for 3 extra dice.