No, the only way is to do cheats or an event, and there are no more events for Pokemon Heart Gold because there is a new Pokemon game they are doing special events on.
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Lugia cannot be obtained as the event to get the item for it has finished.
No, unless you want to use the Action Replay for the Event.
You can't catch Cranidos in the wild or from a special event. You'll need to trade for it from Pokemon Diamond, Pearl, or Platinum.
You cannot catch Palkia in HG/SS. To obtain Palkia u will need to get TRU Arceus to do the Arceus Event in the ruin of alph.
No, but you will be able to catch Palkia, Dialga or Giratina.