The term "coccus" refers to a spherical shape and the term "staphyl" refers to a tendency to group together in clusters. Staphylococcus bacterial species will appear round in shape and tend to cluster together, creating a grape-like appearance.

The term "bacillus" refers to a rod-shaped bacterial species, while the term "spirilli" refers to spiral or helical bacteria. Bacillus anthracis is rod-like in shape. Escherichia coli is also rod-like in shape. Spirillum minus is spiral in shape. 

Recall that the shape of a bacteria classifies the bacteria as either a bacillus, coccus, or spirilla. Bacillus bacteria are rod-shaped, coccus bacteria are spherically shaped, and spirilla bacteria twist into a spiral. Since the researcher observes a spherical shape, the bacteria must be a coccus.

Bacteria classified as coccus often contain the word ‘coccus’ in their names. Of the three bacteria listed, only the Staphylococcus aureus contains the word ‘coccus’ in its name. This means that it is a coccus and, therefore, is a possible identity of this bacteria.

Cytoplasm is found in all types of cells. Flagella is found in all cells that are mobile. Spores can be found in bacteria but also fungi. Ribosomes are found in prokaryotic cells albeit smaller in size compared to those in eukaryotic cells. 

Bright pink cells under Gram stain are characteristic of Gram negative status. This is associated with an outer lipid membrane and reduced peptidoglycan. The reduction in peptidoglycan is what leads to a failure to retain the Gram stain, which would have colored the cells purple.

Gram-positive bacteria are able to retain the crystal violet stain found in gram stain because of their thick peptidoglycan cell walls. Consequently, these bacteria stain dark blue or purple by gram staining. Alternatively, gram-negative bacteria appear red or pink because they are unable to retain the dye due to thinner cell walls and less peptidoglycan.

No animal cells will have cell walls. Trichocytes are specialized to be hard and resilient, but do not have cell walls.

Fungi, plants, and bacteria do use cell walls. The distinction between gram positive and gram negative bacteria refers to the composition of the cell wall only; both positive and negative bacteria have a cell wall present.

Bacterial cells are prokaryotic and lack all membrane-bound organelles. We can thus eliminate mitochondria and nucleus as answers. These structures are not found in bacterial cells or in mature erythrocytes.

All cells, regardless of origin, are surrounded by a cell membrane. This structure is present in both prokaryotes and erythrocytes.

DNA is used to code for the genome of the organism and is found in both prokaryotes and eukaryotes. Bacteria contain a cytsolic genome known as the nucleoid. Red blood cells, however, lack DNA. This is partly due to their lack of a nucleus, and is considered evolutionarily advantageous because no viruses can target red blood cells.

The technique explained in the question is the "Gram stain". Bacteria that are Gram-positive will stain a bluish-purple color, while Gram-negative bacteria will stain a red or pink color. This difference in color occurs because of the large cell wall present on Gram-positive bacteria, and is a response to increased peptidoglycan expression. Additionally, some bacteria (such as mycobacteria and helicobacter) are not easily stained using this method.

Bacilli are rod-shaped bacteria and "strepto" indicates organization in a chain. Streptobacillus bacteria are a class of bacteria that are rod-like in shape and tend to congregate in chains of cells.

Cocci are spherically shaped, and spirilli are rigid helices. Spirochetes are non-rigid helices.

Since the obligate anaerobe grows well, we know that both bacteria are grown in an anaerobic environment.

A facultative anaerobe can grow in an aerobic or anaerobic environment. It simply grows better when oxygen is present; therefore, we would see slower growth from a facultative anaerobe than an obligate anaerobe when there is no oxygen present. If the bacteria were aerobic, it would not grow at all in the anaerobic environment.