What are the specific effects of hidden armor bonuses in Minecraft?

No, Projectile Protection does not reduce knock-back from projectiles.

Yes, Fire Protection's burn time reduction scales with the level. And there isn't a cap.

Explanation:

  1. Protection: Reduces damage from most sources, nothing else.

  2. Fire Protection: Reduces damage from fire AND reduces burn duration.

  3. Blast Protection: Reduces damage from explosion AND reduces knock-back from explosions.

  4. Projectile Protection: Reduces damage from projectiles(ex. fireballs), nothing else