Gambusia need to stay where they are and water will get to cold for guppies to survive well.
It is an offence under sections 52 and 53 of the Biosecurity Act 1993 to sell, offer for sale, display, release, move or breed gambusia
Yes we have a native mantis shrimp you can collect in most estuarine areas in the upper north island.
https://aquariumworld.nz/databases/10-marine/1844-Crustacean-Mantis-Shrimp
Hi 9 tropical species are on the import list
https://aquariumworld.nz/databases/14-Tropical FWFishallowedinNZdatabase/
Some were available from Livin Reef in Christchurch recently but have sold out i think
Natives can be kept but not sold without a permit