Hey,
Bachelor of Science in Biochemistry is a three year long undergraduate programme. It teaches you about chemical and physio-chemical processes.
The basic eligibility criteria is to pass 12th with Science stream.
Yes,you can work as a teacher or professor but you would neet to get a B.Ed degree or M.Sc or P.hd respectively.
You can work in the fields like medical,agriculture,public health care,forensic environment etcetera. You can work in companies like Biotechnology,Food and Drink industries,Research Companies and laboratories,Sales and Marketing firms etcetera.
Hope this helps you.
Good luck.