>>32895113Nuzelock is a set of rules that applies to most trainers to help conserve rarer Pokemon and leave most of the wild populations intact. The only exceptions is that Pokedex holders can catch one of every Pokemon for the purpose of research, and Champions/E4/Gym leaders can catch specific Pokemon for their team.
However despite being able to catch more Pokemon in this positions, catching whatever you want is still taboo and traditionally only using Pokemon you happen to meet is seen as fate and a stronger bond - it was meant to be.
Shinies are allowed to be caught whenever they are seen, since it's known to be a detrimental mutation in the wild.
As far as Pokemon breeding, it's actually very rare for Pokemon to breed in captivity, especially outside of their species.