Learn German: Interessieren Sie sich für Kunst?

In German, the verb sich interessieren is reflexive. While in English you use "interested" as a description, in German you use an active verb and literally say that you "interest yourself". Since the subject here is the formal Sie (you), the matching accusative reflexive pronoun is sich.

Why does the sentence use für instead of a German word for "in"?

Reflexive verbs often team up with specific prepositions, and they rarely translate word-for-word. The verb sich interessieren is always paired with für (literally "for"). It is best to memorize the whole chunk as a set phrase: sich interessieren für (to be interested in).

Why does sich come after Sie instead of staying right next to the verb?

In a yes/no question, the conjugated verb must come first (Interessieren), followed immediately by the subject (Sie). The reflexive pronoun (sich) has to wait its turn and takes the third slot. If you changed this into a normal statement, the subject would come first: Sie interessieren sich für Kunst.

Does the accusative reflexive verb make Kunst accusative too?

Kunst is indeed in the accusative case here, but not because of the reflexive verb! It is accusative because of the preposition für. The word für is a "strict" preposition that always requires the noun following it to be in the accusative case, no matter what the rest of the sentence is doing.