Latios is a non-breedable Pokemon,so no.
You can find Latios on Pokemon Emerald, Ruby, and SoulSilver.
Yes, Mewtwo, Latios and Latias will be in HeartGold and SoulSilver.
latios is a roaming Pokemon so it will appear in random places in kanto
No, neither Latias nor Latios are breedable.
You get emerald and choose blue, have sapphire, have soulsilver.
Entie,Rioku,and Suicune, also Latios in the kanto region
by migrating pokemon from your gba game
after catching latias/latios YOU DO NOT HAVE TO CATCH LATIAS/LATIOS TO MAKE A HUT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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).
After catching Latios, you might want to focus on catching all of the other legendary Pokemon, for example, the roaming Latias and the roaming Raikou and Entei. After catching all of the legendary Pokemon, the only thing left to do is to fill your Pokedex, which is nearly impossible.
at the National Park