No, Chao in school don't age. Chao only age when you are in the garden with them.
Hero Garden fruits seem to be glitched, they're giving my Chao two or three blocks of Stamina per nom instead of one so I'm getting a level up from every fruit! It took ages to get my Chao up to 20 stamina in the neutral garden yet earlier today I got a newborn to 16 from Hero fruits alone.
So yeah, evolve a Hero Chao and move upstairs as soon as possible.
According to http://chao.hippotank.com/sa2b/fruits
they definitely should not be doing this, the regular neutral, hero and dark fruits are supposed to be different in appearance only,