Send him into a city and stay there until you get the "is fully rested" message. Or splash out on salt pork and healing potions.

Yes.

Thanks!

Also spell, 15 mana maybe? that will heal the entire stack.

I think there is a special equipment piece you can research that gives a unit you equip it with some sort of healing powers but you have to reasearch it.

There is a Healing Pack that you can put on your units.  It's quite expensive and gives a +1 Health Regen and +5 Health for 25 gold and 2 material per unit.  The description is "this pack contains various items used by medical practitioners."  I just got to the point where I've put it on a few units, but haven't really had much of a chance to experiment with it.  I suspect that's health regen on that specific unit only though in spite of the name and description.  I also don't know if this works both in and out of combat.

There's also a Health spell domain which you can unlock if you research far enough up the Magic tech tree.  Again, I haven't had much of a chance to experiment with it, but as far as I can tell the Heal spell only works in combat.  There's also a Mass Heal which I haven't researched yet.

There's also a healing potion and salt pork available at town stores which replenish five hit points whenever you use them. Just like any other RPG, if you want to go on an epic adventure, it pays to stock up on the healing potions first