The very fine whirled one under the grey rock looks a bit like hornwort. It's illegal to take or keep this plant.
I'd burn it, it's the safest way to dispose of it.
Our local waterways have a few pest plants in them. The problem is they look quite good!
It's our responsibility to make sure we don't use any pest plants in our tanks. You local regional council has a little book called 'The Pest Plant Manual" which lists all the plants you're not allowed to keep.
There's a whole pile of NZ plants that work well in aquariums (both coldwater and tropical). Good on you for trying but I'd dispose of the hornwort.
I'll look up the others to see if there are any more pest plants in your photo.
It's important to note; being caught with pest plants can land you a fine between $5,000-$200,000 or even a nice stay in prison...
A pest plant is one that out-competes the NZ native species and displaces them. NZ has a strong drive to keep it's native species, it's part of make our country unique. It's our job to make sure we don't accidentally spread these problem plants.