Let me see if I can explain this to you bit by bit. When you learn something from someone, the benefits, gains and advantage usually come from the suject matter but in many cases the person who teaches you can have an important role and can make the difference for you in relation to studying under a different teacher.
Art is one of those subjects in which the teacher has a a very important role in the outcome. Choosing the right teacher can really make a difference both in terms of actual knowledge bit also about contacts and connections. Art students who studied under Peter Paul Rubens probably had a more successful career than those who studied with other teachers.
Your answers 1-3 seem to be related to something "extra" in addition to learning art (prestige, reputation, contacts, future financial gains, access to resources, etc.) while 4 seems to be related directly to the specific knowledge the teacher can pass on to the student regarding the subject matter.
Benefits, gains or advantages can be used interchangeably depending on the intention of the speaker.
Your questions are very direct, seem to indicate that the teacher is to provide something directly to the student:
What benefit can I get from you? (A scholarship?)
What can I gain from you? (Prestige?)