Science

You will have to check with the institute which offer admission in MPH, as different institutes have different eligibility criteria for admission into their MPH courses. Please refer to the link provided below for a list of colleges which offer admission into MPH, and their eligibility criterias:
https://www.shiksha.com/medicine-health-sciences/colleges/mph-colleges-india

You will need to wait for the next cut-off list to see if you have a chance to get through to Shyamal College.

Very very less. You must go for Masters. Today, every biological subject gets it's value after Masters. After that, you can go for any big company.

Please refer to the link provided below for a detailed list of entrance exams which are required to clear for admission into a course in MS in India:
https://www.shiksha.com/engineering/articles/m-tech-entrance-examinations-in-india-blogId-12539

Focus on getting good grades in your B.Sc undergraduate study. Once your B.S.c is completed it will open up numerous avenues in the industry which you can pursue. You could also opt to do an M.Sc. which will increase your knowledge base and improve your marketability. B.Sc. has immense scope in the industry and you should focus on studies to get better grades, and prepare for placements, if you want a decent job after your under graduation.

Please refer to the link provided below for details on the institute in question. You will find all details you need through this link:
https://www.shiksha.com/college/st-pauls-institute-of-communication-education-bangalore-52170

Yes, you may appear for NID entrance exam for the Masters degree.