The author doesn’t use conditional reasoning, so there isn’t a confusion of sufficient and necessary conditions.

The argument doesn’t overlook this possibility — it acknowledges that Costa seems to hold contradictory views. The flaw is the failure to recognize that holding contradictory views does not prove one of those views wrong.

The author rejects C’s reasoning based on the grounds that C’s criticism (that assigning works of art to period styles doesn’t make sense) could be applied to C’s own theories. This is a flaw, because holding contradictory views doesn’t establish one of those views is wrong.

(D) describes a whole-to-part fallacy. The author’s premise isn’t a statement about art generally. The author’s conclusion is not an attempt to apply a feature of art in general to every type of art.

The author does not assume that theories about one art cannot be compared to theories about another art. In fact, the author seems to think Costa’s argument concerning baroque and neoclassical Austrian painting is relevant to theories on French opera.