1. I get the feeling of anime battle school genre from this, so I'd lean towards the PCs being teenagers. By the time they're adults, it feels like they'd be out in the world doing noble shenanigans rather than just doing more schooling, really.

2. I have a whole buncha systems that I've tried out in the past. A D20 is pretty high variance from my perspective; the 2d6 systems that are more common in Japanese TTRPGs are generally more stable. If you want to push a bit further, you could introduce a stats system too.

3. In an RP I'm currently, I basically had every PC create three or so NPCs that had some tangential relationship with their character. If you apply it here, it'd be easier to generate the NPC pairs and also make the school actually feel like a school where we at least kinda know everything. Allows for more simulated drama as well.

4. Slice of Life school hijinks don't make much sense for Nobles and their Knights. I'd say that we can have low-stakes competitions and shenanigans to start, but there should be a gradual ramp-up of drama and conflicts. Shadow governments, revolutions, etc.

5. From a purely RP perspective, I feel like it'd make more sense for Nobles and Knights to fight together in Duels. Like, Nobles provide support magic and offensive ranged attacks, while Knights serve as frontline combatants that protect their Nobles. The concept of the Duels isn't to prove that you're a stronger Knight, but rather that you're a Knight who's more capable of protecting your Noble from danger. So the win-con would be inflicting an injury on the enemy Noble, rather than just beating the enemy Knight. Nobles probably have something like a magical barrier cast upon them by the overseeing professor, so they don't risk actual injury.

6. Off the top of my head, Hoshimi Junna and Tendo Maya from Revue Starlight are easy favs of mine. Recent favorite would be Takamatsu Tomori from Bang Dream Its MyGo!!!!! too.