Dual

Dual would be a deadly combo. Although both are equally good and you should go according to your area of interest.

Presidency College does not offer dual specialisation. The fee structure of MBA is around 2 lakhs per annum.

Hi,
It doesn't matter if you do it even from a top institute because you are not working. You should do it only if you are employed and have around 2 years of work experience. Fully online MBA is not allowed as UGC has banned it. You may go for the following institutes:
Pondicherry University,
Anna University,
Bharati Vidyapeeth,
Kurukshetra University,
University of Madras.
Do not opt for any private university and universities from Rajasthan, north India, Bengal and north east states including Sikkim. Always prefer a part time program.

No, combined B.Tech + M.Tech is equally valued as compared to separate B.Tech and M.Tech.

You can get all the information about choosing astrophysics as a career. In India, you can pursue it at IISC Bangalore, Pune, Punjab university etc. Explore this:
http://www.iiap.res.in/opportunities/career

Yes, recent trends of management are inclined towards dual specialization. You can do that but try to take your subject electives regarding those area and be up to date in those sectors.

HR is not offered as major it's only offered as minor .But you can take 2 majors out of Marketing/Finance/Business analytics/Operation