ПŽ€ You have to swap every Pokémon you catch with one of the eggs that are in your PC, and use the Pokémon that hatches from there instead. ПŽ€ As for the catches, it's still like in a nuzlocke: as soon as you get your Pokéballs, you may only catch the first Pokémon you find in each area. It creates a stronger bond between you and them! ПŽ€ You also must nickname all the Pokémon that you will use in your team, if they don't already have a name. You can box them or release them, your choice.
ПŽ€ This is still a nuzlocke, so every Pokémon that gets knocked out is considered dead, and cannot be used in battle ever again.