1. No corrections needed
This sentence does not need a comma because the subject for the verb analyze is at the beginning of the sentence, not after the conjunction and.
2. The history of rap music is interesting, and so many musicologist are beginning to examine it.
This sentence is a compound sentence. It is made up of two independent clauses joined together with the conjunction and. Since there is a subject-verb phrase in both parts there must be a comma before the and.
3. Hip-hop is related to rap music, but they are different in some ways.
This sentence is also a compound sentence and needs a comma before the conjunction but.
4. Because of it's proximity to the San Andreas Fault, San Francisco experiences many earthquakes.
This sentence contains a dependent clause and an independent clause. Since the dependent clause (Because of it's proximity to the San Andreas fault) is before the independent clause a comma is used to separate them. If the dependent clause was after the independent clause, there would not be a comma between them.
5. No corrections.
This is the same reasoning as number 4.
