Learn German: Die Begeisterung für die Band ist riesig. - The enthusiasm for the band is huge.

The noun die Begeisterung (enthusiasm) has a fixed prepositional object: für plus the accusative case. Just like in English where you have enthusiasm for something, German uses für. Since für is strictly an accusative preposition, the noun follows as die Band.

Does the verb form of this noun use the same fixed preposition?

Yes! The related reflexive verb is sich begeistern für (to be enthusiastic about). For example, you would say Ich begeistere mich für die Band. The fixed preposition für carries over directly from the verb to the noun.

Band is an English word. How does it get its feminine gender (die Band)?

English loanwords often adopt the gender of their closest German equivalent. Band (meaning a music group) is feminine because the German word die Gruppe is feminine. Be careful not to confuse it with the native German neuter noun das Band (the ribbon or tape).

Why does riesig not have an adjective ending like -e or -er here?

Here, riesig (huge) is used as a predicate adjective, meaning it comes after the verb ist to describe the subject. In German, predicate adjectives never take declension endings. It would only get an ending if it were placed directly before a noun, such as in eine riesige Begeisterung.