no moltres doesnt respawn. But before you take any legendary pokemon on always save the game just in case you want to catch it but you make it faint.
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Nope.
Yes, all 3 of them (Articuno, Zapdos and Moltres) will be in Pokémon HeartGold and Pokémon SoulSilver.
The cool legendaries you can get in Soulsilver/heartgold are the following: Lugia, Ho-oh, Raikou, Entei, Suicune, Articuno, Moltres, Zapdos, Mewtwo, Latias, Latios (Latios in Soulsilver & Latias in Heartgold), Kyogre, Groudon, Rayquaza (Kyogre in Heartgold, Groudon in Soulsilver & Rayquaza if you have both).
You have to soft reset for it.To soft reset your ds press start,select,l and r buttons.Depending on how lucky you are,you could get it on your first try or you could SR forever and never get one.I wish you luck on trying it,and I'm soft reseting my DSIXL to get a shiny moltres in soulsilver right now.Good luck once again!
If you mean how to consider yourself as beaten the kanto region in pokemon soulsilver, then you should find zapdos,moltres, and articuno. You should also beat Red (Ash Ketchum). Once you do that, you can catch Mewtwo.