Does the max amount of HP and AP increase when I level up?
Max HP and AP levels do not change as you level up. These stay consistent throughout the game to keep gameplay simple across all the classes you're playing in.
Instead, you "grow" by unlocking new powers and accessing cooler gear for your characters as you level up.
Warriors, Mages, and Healers have unique strengths and weaknesses, including their different stats. This makes it important for you to work together with your teammates! For example, Warriors have low AP but high HP, Mages have high AP but low HP, and Healers are slightly more balanced in terms of each.