I put a link to a guide all about legendary pokemon in HeartGold in the related links.
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I don't think you can refight any legendary Pokemon except the wandering dogs.
You can't. They all run away and you have to run around the region to try to catch them. In the wild grass.
well depends if it is a boy and girl then yes but if i doesnt tell then no
It's not the "last" Legendary Pokemon that you can find in Pokemon HeartGold, but most people usually catch that one last given that you need to have both Kyogre and Groudon in your party for Professor Oak to give you the Jade Orb to get to Rayquaza.
It will be very unlikely.