Yes, it's normal
Inside the Battle Tower you can't regenerate HP or MP.
But if you really wish to regenerate at a save place, take the Throne Room Teleporter Scrine to a save location (but if you play FoV part, this Scrine is stuck!).
For the Dragon: you only regenerate Mana, not HP. So you can switch between both forms (dragon <> human) to make faster work for having back a full HP bar (drinking healing potions as a dragon I always try to NOT need it, so I put at least as fast as possible 2 or more points into skill Dragon Spirit ! - it's faster to drink/eat in human form + if you Strength is high and you've some equipment with Healing Aura you reg. very fast HP
Happy Hunting
