Well, catching Pokemonz is the same as any other RPG. You fight them, and leave the post with the Pokeball shaking. Ill flip a coin for if you caught it or no. You SHOULD have Pokeballs with you, but if not, you can find them throughout the Sun Region.
Legendary Pokemon CAN fight with you, but only if you have the Soul orb, which is what the Team is looking for in the clearing. The Soul Orb makes another part of the Soul (and your Guardian is now part of your Soul) real, which is what the Team is misunderstanding. They think they can control what their souls desire. ;] There are SEVEN Soul Orbs around the Sun Region. Only ONE is in the clearing. ;] And since your mind is a kind of telepathic power, you are able to teleport your Guardian from where they are, to where you are. (Hope this isn't confusing.)
Does that helpp?