From the wiki article:
However, unlike terrestrial communities, where most autotrophs are plants, phytoplankton are a diverse group, incorporating protistan eukaryotes and both eubacterial and archaebacterial prokaryotes.
The fact that they're named after plants, does not make them plants.
Microscopic organisms probably contribute at least half of the photosynthesis-produced oxygen in the world, but produced a lot more early on in the Earth's history and allowed for the development of more advanced organisms at all.
The water? I'm not sure, I believe from icy foreign bodies is one common theory, but it's irrelevant, because water life came first (and, you know, plants need water too).