Mi amigo asiste a la clase de música los viernes.

Asistir a means “to attend” or “to be present at.” It’s always constructed with the preposition a before the event or place you attend:
• asistir a la clase – to attend the class
• asistir a un concierto – to attend a concert
You cannot drop the a (i.e., asistir la clase is incorrect).

Yes, but each verb has a slightly different nuance:
• va a la clase (he goes to class) – focuses on the act of going there
• asiste a la clase (he attends the class) – emphasizes participation/attendance
• toma la clase (he takes the class) – very common in Latin America, influenced by English “take a class”
All are grammatically correct; choose based on the shade of meaning you want.

a la is formed by combining a (to) + la (the, feminine). Clase is a feminine noun, so you use la.
al (a + el) would be used only with masculine singular nouns, e.g., al examen (to the exam).

Spanish indicates the subject of a class with clase de + [subject]:
• clase de música – music class
• clase de matemáticas – math class
You cannot invert it to música clase. You might also see clase musical, but that generally describes a type or style of class rather than “a class about music.”

los viernes means “on Fridays” (repeatedly). The plural definite article los plus the day expresses a habitual or routine event:
• los lunes – on Mondays
• los fines de semana – on weekends
If you refer to one specific Friday, you’d say el viernes (this Friday).

In Spanish, the simple present tense often covers habitual actions.
• Mi amigo asiste – My friend attends (as a routine).
The present progressive (está asistiendo) would highlight that he is attending right now, at this very moment, not as a regular schedule.