Dual

For Integrated MBA, IIM Indore conducts the entrance exam and other institutes may take entrance as per their policy or take admission on the basis of merit also.

IISER and NISER are the best universities.

For integrated biotechnology, NEET is not needed they will have separate exam for that colleges which are offering for this course includes GITAM and some reputed universities which are varied for every three to four years.

See there's good chance to get admission to a well ranked institutions abroad because of the belief that Tezpur University boast of having good practical, industrial and academic exposure. After pursuing same you have same opportunities as any other Ph.D holder but in many after Ph.D prospects like a professor, research associate, etc you have a good preference on the basis of your academic performance.

Yes, BCA+ MCA is a hot career now a days.

I would say IIIT, Allahabad, since it has a better reputation in terms of placement and infrastructure. Both are really good choices and there is no doubt about that though.