The in-game legendaries are Ho-oh, Luigia, Mewtwo, Entei, Raikou, Suicune, Moltres, Articuno, Zapdos, Latias, Dialga, Giratina, and Palkia (Dialga, Palkia, and Giratina can only be received if you have 12th Movie Arceus, but you can only choose 2 of the 3). The legendaries that you can receive by Mystery Gift are Mew, Latios, Jirachi, and Celebi ( Celebi is at GameStop from February 21, 2011 until March 6, 2011).
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The PokeWalker allows you to walk with a select Pokemon from your copy of HeartGold and if you walk enough, you can capture extremely rare Pokemon (though not legendary).
Yes, you can trade Legendary Pokémon as well as any other Pokémon from Pokémon Platinum over to Pokémon HeartGold, you just need the regional PokéDex in both trades before you can trade.
Aura Beam is in Pokemon HeartGold.
That is impossible in Pokemon HeartGold and SoulSilver.
there are many legendary Pokemon in Pokemon heartgold, but the best is HO-OH
I put a link to a guide all about legendary pokemon in HeartGold in the related links.
In HeartGold you can catch Kyogre.
Articuno
mew
I don't think you can refight any legendary Pokemon except the wandering dogs.
migrate and trade
Kyogre is only available for Pokemon: Sapphire on the GBA. Ho-Oh is the legendary pokemon available to you in HeartGold.
No legendary can lay an egg except for manaphy which gives an egg to phione and you can not get manaphy or phione in heartgold
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Ho-ohLugiaCelebiJirachiLatiasLatiosSuicuneRaikouEnteiZapdosMoltresArticunoMewtwoKyogre-HeartgoldGroudon-SoulsilverRayquazaPalkiaDialgaGiratina
Moltres is the only legendary Pokemon in Mt. Silver for HeartGold / SoulSilver only.