Lord Ruby I wasn't clear if by 'strongest Pokémon still standing' you mean 'most HP remaining' or 'highest level' so I went with the option that would let me wrap up the fight. Hope that's okay.
And to be absolutely clear: you can catch wild Shadow Pokémon, the dice just weren't cooperating in this case.
Also I think Flotsam stole your Luxio. (Don't fret, they're a pretty common Pokémon in the area you're in.)
Kind of. They're ancient artifacts, so they aren't very durable and will break after a number of uses.