M.Sc

Since, you have done M.Sc in biotechnology, you can do MBA in biotechnology also. MBA in hospital administration is also good. But, as your background is M.Sc in biotechnology, I would suggest you to pursue MBA in biotechnology.
You can consider the below mentioned institutes:
1. Amity Institute of Biotechnology.
2. Bharati Vidyapeeth University, etc.
You can visit the below mentioned link:
https://www.way2college.com/

Hello,
You can check the below mentioned institutes:
1. Technology Information Forecasting and Assessment Council (TIFAC).
2. National Human Rights Commission (NHRC).
3. Indian Academy of Sciences Summer Research Fellowship.
If you are willing to pursue your career further as a junior research fellow or an assistant professor, then you can also prepare for CSIR NET exam, which is conducted for the science students twice in a year.
You can check the below mentioned link for the cutoff of CSIR NET:
https://scoop.eduncle.com/csir-net-result-cut-off-marks
Best of luck.

This section is to entertain queries for MBA at BITS, Pilani. You should post in your respected section. But, in my opinion, you have to clear BITSAT exam to get admission for M.Sc.

Yes, you can pursue M.Sc in astrophysics but only in theoretical astronomy. For others, engineering is required to pursue higher studies in this. You can refer to below article for this.
http://indiaeducationdiary.in/career-options/Science-Astrophysics-Eligibility.asp

Yes, you can opt for PhD abroad. There are so many opportunities available for you.

Among your choices, my recommendation will be as follows: M.Sc. in CS or IT, MBA and MSW. You are advised to choose the subject for your PG based on your interests to excel in your chosen career.

It is quite impossible. If you have done B.Sc. in nursing then it is possible but B.Sc. in any other specialisation is not a requisite criteria to go for M.Sc. in nursing.