Is Amoeba phytoplankton or zoo plankton?

Neither, but closer to zooplankton than phytoplankton in my book.

PLANKTON is not a taxonomic term. Plankton are organisms that can not actively swim against currents. Contrast "plankton" (floaters) with "nekton" (swimmers). ZOO -plankton are animal floaters like copepods and jellyfish, whereas PHYTO-plankton are photosynthetic floaters that include single microscopic cells like diatoms and dinoflagellates (organisms that make red tides). Amoeba are protists in the domain Eukarya so are more related to animals than plants, but are neither.