Typically when you attack someone (campaign and multiplayer) and deploy your troops, the remaining troops dissolve back into elixir and you don't get to keep them. They don't return home.
If I deploy my hero when attacking, will HE COME HOME after the battle???? I don't want to have to spend another 10,000 of dark elixir to get him back.
The barb king has a different mechanic to them. He is persistent and will return to your base, but he must heal any damage he recieves. This cool down increases as he levels.
If he recieves no damage, no cool down is necessary.
"Hereos are immortal and only need to be purchised once."
Once you get him, you can use him forever for free (although upgrades do cost de; a lot). If your lvl 1 BK's health drops to 0 in battle you will need to wait 60min before you can use him again. If he takes no dmg, you can use him again immediately. He can also be set on guard mode to defend your village.