I changed my mind. There is a right way to play, and it's my way.
Constructs do not heal. They get repaired. If they are unable (for whatever reason) to repair themselves, or if they are not repaired by someone/something else, they do not gain HP back. A construct doesn't have morale, or luck, or other things that make up HP any more than a car has morale or luck.
Undead: they do not heal unless they have a source of power that grants the healing. Vampires drink blood, Lich's can channel magic, ghosts suck life, etc.
Living creatures: Just like any other living creature.
There. I have spoken, and this is my decree. It is the only right way to play D&D. You are welcome.
Thank you...I can finally go to sleep now.
/grin