The Revenge of Monster Magnet!

Yes they will. It's called that little arrow button next to you HP on the stats screen.

Woohoo, either cripple your character to the point that it's doing 3rd job damage at level 180 (and thereby being completely useless for attacking) or HP wash with int gear costing billions and spend nearly one million NX (even with MTS, this is a daunting amount), just for the sake of surviving one boss. Hm, no thanks.

You should never have to invest AP into HP. People who don't play ranged classes are so nonchalant about the idea of being 1hkoed, like it's not frustrating at all to have to spend a ton of money just to ensure that a tombstone won't fall over your head the moment you walk into a boss chamber, regardless of how skilled you are at playing your character.