The first image is of a female guarding her nest during a shower of rain. She is probably of the Dolomedes aquaticus species. She will protect her nest until her spiderlings eat their way out.
This spider is the same species but sitting on a water lily leaf. They are quite large spiders and they walk on water. They don't construct webs to catch insects, but use the water surface as a web, feeling for vibrations of insects struggling on the surface and then running across the surface to seize their prey. Apparently they can inflict a painful bite, but it is not dangerous.
If you have spiders in your garden that you would like to identify, check out Te Papa's What Spider is That? page.