a) the area is one of the best in Argentina.
b) BA is a world-class city, think Paris, NYC, Berlin. Yes it is possible to live alone in the city, but I think it would be better to share a flat with other foreigner or local students.
c) It is feasible. Maybe you could live in the middle between those areas: Belgrano and/or Nuñez, very good neighborhoods with everything at your disposal. You have also trains to reach the northern suburbs, which are quick, safe and cheap.