The noun is “car.” The noun “car” in the example also is a subject complement, which we discuss in our post Subject Complements: Usage and Examples.

The word “those” refers to the eyes of the grasshoppers and katydids in your sentence. An even clearer way to write it would be:
The eye of the cricket investigated here is similar to that of the grasshopper and katydid. (consistent singular references)
or
The eyes of the cricket investigated here are similar to those of the grasshopper and katydid. (consistent plural references)

Determiners are a wider category of grammar. As the article discusses, demonstrative adjectives concern the words “this,” “that,” “these,” and “those.”

Determiners are NOT adjectives.

A demonstrative pronoun stands alone. A demonstrative determiner precedes a noun.

Yes, a single pronoun forms a noun phrase. A single noun can also form a noun phrase.

A single pronoun does not qualify as a noun phrase.

This is what I want because I like it.

Yes, “that” is a demonstrative pronoun, and its antecedent is “financial situation.” The phrase “of the Joneses” does not require an apostrophe. Using “of the” makes the phrase possessive without the apostrophe.

The Smiths’ financial situation is similar to that of the Joneses.

Also, is “Joneses” correct as written (plural but not possessive), or should it be “Joneses’ ” (plural and possessive)? I’m guessing that it is correct as is because the use of “that” (or “that of”) obviates the need for “Joneses” to be possessive—but I’m not sure. Kindly advise.