Biological Classification

Thermococcus, Methanococcus and Methanobacterium are archaebacteria (archaea).
Methanococcus and Methanobacterium are methanogens, which produce methane, and Thermococcus is a thermophile living at very high temperatures.
These archaea belong to the group Euryarchaeota, whose DNA is wrapped around proteins that are homologous to the core histones (H2A, H2B, H3 and H4) of eukaryotes.
Their DNA is relaxed or positively supercoiled, which helps to stabilise it at high temperature.
Being prokaryotes, they do not have mitochondria or other membrane-bound organelles, so the statements describing them simply as bacteria with a cytoskeleton and mitochondria are wrong.
So they exemplify archaebacteria that contain protein homologous to eukaryotic core histones.

Diatoms have a cell wall of two overlapping silica halves (frustules). At each vegetative division the daughter cells become progressively smaller.
The original size is restored by the formation of auxospores, usually after sexual reproduction; auxospores are formed by several (most) diatoms.
Hormocysts are multicellular, thick-walled resting structures formed at the ends of filaments in a few cyanobacteria, such as Westiella and some members of the Stigonematales.
On germination they give rise to new filaments.
So auxospores are formed by several diatoms and hormocysts by a few cyanobacteria.