Western Springs Lake suffers from algae blooms from all the bread and bird poop in the water. They leave them just like the Koi to keep the water clean.
Play sand will be safe for your Kuhli's but you will have to wash it about 5 times. Go check out stone and water world, they have fairly cheap sand in a range of colours.
The catfish have been there for the last 5 years or so. It is a closed lake/stream system meaning the catfish cannot travel to other water ways. They have just culled the geese recently (last year) but they are still annoying.
Depends what airport you are departing from/stopping over at. Auckland they x-ray u bags as well as Wellington and CHCH. They are usually ok with coffee and stuff but i don't know if they would let you take on a box of fish.