You can't get a Pokemon that been fainted.
So if you killed a Ho-Oh in Heart Gold, you wouldn't seen again.
Using a Master Ball is good to catch a Ho-Oh in Heart Gold.
You can get one after you beat all gym leaders in Jotho, go back to New Bark Town in Prof. Elm's lab.
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You bet
It is gone. If you saved the game after you killed it then it is gone forever.
the fog badge and the rainbow wing
yes you can. but if you have Pokemon soulsilver, the first encounter will be a lugia and vice versa for ho-oh.
They are not in Pokemon HeartGold