What should a student know about B.Sc (Mathematics) in terms of research, academics, and teaching?

You should master mathematics of 11th and 12th standard first and then take admission in a good college.

If you are taking of mathematics, then I suggest you to first clear your concepts of basic maths of your school syllabus first. There is time for the research, teaching purpose, you will get to know when you start your career and graduation.