Do protists represent a group of organisms that... (continued in details)?

> Do protists represent a group of organisms that.... share common adaptations and ancestry as suggested by inclusion in a single kingdom?

Nope. Protista was a catch-all grouping of eukaryotic organisms that weren't a good fit for Animalia, Plantae, Fungi. It's not a clade. It's not monophyletic.

No.

The only common features are the absence of complex tissue differentiation. The protists are an extremely diverse group, more diverse than plants animals and fungi combined.

Origin of eukaryotes

Probably through symbiosis

Anaerobic and aerobic bacteria present

Some bacteria able to photosynthize to create their own CHO, releasing oxygen into the environment, making conditions difficult for the many anaerobic bacteria

Anaerobic bacteria may have engulfed aerobic bacteria, who had enzymes for obtaining energy in presence of oxygen -- became ancestors of mitochondria

Other bacteria may have engulfed photosynthetic bacteria in order to acquire ability to photosynthesize -- became ancestors of chloroplasts

There are several steps in the origins of the Eukaryotic cell type:

Autogenous membrane development suggests that eukaryotic cells evolved by specialisation of internal membranes derived from prokaryotic plasma membranes. In this model most endomembranous structures are believed to have differentiated from invaginations of the prokaryotic plasma membrane. The double-membrane organelles (mitochondria and chloroplasts) may have evolved by secondary invagination or more complex membrane folding.

Endosymbiotic model holds that certain prokaryotic species, called endosymbionts, lived within larger prokaryotes. This model focuses mainly on the origin of the mitochondria and chloroplasts. Chloroplasts are thought to have descended from endosymbiotic photosynthesising prokaryotes living in larger cells. Mitochondria are postulated to be descendants of prokaryotic aerobic heterotrophs that may have been parasites or undigested prey of larger prokaryotes. The association progressed from parasitism or predation to mutualism.